The gutter and smooth drainpipe in Fig. P6.47 remove rainwater from the roof of a

An engineer claims that the fl ow of SAE 30W oil, at 208C, through a 5-cm-diameter smooth pipe at 1 million N/h, is laminar. Do you agree? A million newtons is a lot, so this sounds like an awfully high fl ow rate.

The present pumping rate of crude oil through the Alaska Pipeline, with an ID of 48 in, is 550,000 barrels per day (1 barrel 5 42 U.S. gallons). (a) Is this a turbulent fl ow? (b) What would be the maximum rate if the fl ow were constrained to be laminar? Assume that Alaskan oil fi ts Fig. A.1 of the Appendix at 608C.

The Keystone Pipeline in the chapter opener photo has a maximum proposed fl ow rate of 1.3 million barrels of crude oil per day. Estimate the Reynolds number and whether the fl ow is laminar. Assume that Keystone crude oil fi ts Fig. A.1 of the Appendix at 408C.

For fl ow of SAE 30 oil through a 5-cm-diameter pipe, from Fig. A.1, for what fl ow rate in m3 /h would we expect transition to turbulence at (a) 208C and (b) 1008C?

In fl ow past a body or wall, early transition to turbulence can be induced by placing a trip wire on the wall across the fl ow, as in Fig. P6.5. If the trip wire in Fig. P6.5 is placed where the local velocity is U, it will trigger turbulence if Ud/ 5 850, where d is the wire diameter [3, p. 388]. If the sphere diameter is 20 cm and transition is observed at ReD 5 90,000, what is the diameter of the trip wire in mm? P6.5 D Trip wire d U

For fl ow of a uniform stream parallel to a sharp fl at plate, transition to a turbulent boundary layer on the plate may occur at Rex 5 Ux/ < 1 E6, where U is the approach velocity and x is distance along the plate. If U 5 2.5 m/s, determine the distance x for the following fl uids at 20C and 1 atm: (a) hydrogen, (b) air, (c) gasoline, (d) water, (e) mercury, and (f) glycerin.

SAE 10W30 oil at 208C fl ows from a tank into a 2-cmdiameter tube 40 cm long. The fl ow rate is 1.1 m3 /hr. Is the entrance length region a signifi cant part of this tube fl ow?

When water at 208C is in steady turbulent fl ow through an 8-cm-diameter pipe, the wall shear stress is 72 Pa. What is the axial pressure gradient (p/x) if the pipe is (a) horizontal and (b) vertical with the fl ow up?

A light liquid ( < 950 kg/m3 ) fl ows at an average velocity of 10 m/s through a horizontal smooth tube of diameter 5 cm. The fl uid pressure is measured at 1-m intervals along the pipe, as follows: x, m 0 1 2 3 4 5 6 p, kPa 304 273 255 240 226 213 200 Estimate (a) the total head loss, in meters; (b) the wall shear stress in the fully developed section of the pipe; and (c) the overall friction factor.

Water at 208C fl ows through an inclined 8-cm-diameter pipe. At sections A and B the following data are taken: pA 5 186 kPa, VA 5 3.2 m/s, zA 5 24.5 m, and pB 5 260 kPa, VB 5 3.2 m/s, zB 5 9.1 m. Which way is the fl ow going? What is the head loss in meters?

Water at 208C fl ows upward at 4 m/s in a 6-cm-diameter pipe. The pipe length between points 1 and 2 is 5 m, and point 2 is 3 m higher. A mercury manometer, connected between 1 and 2, has a reading h 5 135 mm, with p1 higher. (a) What is the pressure change (p1 2 p2)? (b) What is the head loss, in meters? (c) Is the manometer reading proportional to head loss? Explain. (d) What is the friction factor of the fl ow?

A 5-mm-diameter capillary tube is used as a viscometer for oils. When the fl ow rate is 0.071 m3 /h, the measured pressure drop per unit length is 375 kPa/m. Estimate the viscosity of the fl uid. Is the fl ow laminar? Can you also estimate the density of the fl uid?

A soda straw is 20 cm long and 2 mm in diameter. It delivers cold cola, approximated as water at 108C, at a rate of 3 cm3 /s. (a) What is the head loss through the straw? What is the axial pressure gradient p/x if the fl ow is (b) vertically up or (c) horizontal? Can the human lung deliver this much fl ow?

Water at 208C is to be siphoned through a tube 1 m long and 2 mm in diameter, as in Fig. P6.14. Is there any height H for which the fl ow might not be laminar? What is the fl ow rate if H 5 50 cm? Neglect the tube curvature. P6.14 Water at 20 C L = 1 m, d = 2 mm H

Professor Gordon Holloway and his students at the University of New Brunswick went to a fast-food emporium and tried to drink chocolate shakes ( < 1200 kg/m3 , < 6 kg/m-s) through fat straws 8 mm in diameter and 30 cm long. (a) Verify that their human lungs, which can develop approximately 3000 Pa of vacuum pressure, would be unable to drink the milkshake through the vertical straw. (b) A student cut 15 cm from his straw and proceeded to drink happily. What rate of milkshake fl ow was produced by this strategy?

Fluid fl ows steadily, at volume rate Q, through a large pipe and then divides into two small pipes, the larger of which has an inside diameter of 25 mm and carries three times the fl ow of the smaller pipe. Both small pipes have the same length and pressure drop. If all fl ows are laminar, estimate the diameter of the smaller pipe.

A capillary viscometer measures the time required for a specifi ed volume of liquid to fl ow through a small-bore glass tube, as in Fig. P6.17. This transit time is then correlated with fl uid viscosity. For the system shown, (a) derive an approximate formula for the time required, assuming laminar fl ow with no entrance and exit losses. (b) If L 5 12 cm, l 5 2 cm, 5 8 cm3 , and the fl uid is water at 208C, what capillary diameter D will result in a transit time t of 6 seconds? P6.17 Large reservoir l L D

SAE 50W oil at 208C fl ows from one tank to another through a tube 160 cm long and 5 cm in diameter. Estimate the fl ow rate in m3 /hr if z1 5 2 m and z2 5 0.8 m. P6.18 (1) (2)

An oil (SG 5 0.9) issues from the pipe in Fig. P6.19 at Q 5 35 ft3 /h. What is the kinematic viscosity of the oil in ft3 /s? Is the fl ow laminar? 424 Chapter 6 Viscous Flow in Ducts P6.19 10 ft L = 6 ft D = 1 2 in

The oil tanks in Tinyland are only 160 cm high, and they discharge to the Tinyland oil truck through a smooth tube 4 mm in diameter and 55 cm long. The tube exit is open to the atmosphere and 145 cm below the tank surface. The fluid is medium fuel oil, 5 850 kg/m3 and 5 0.11 kg/(m ? s). Estimate the oil flow rate in cm3 /h

In Tinyland, houses are less than a foot high! The rainfall is laminar! The drainpipe in Fig. P6.21 is only 2 mm in diameter. (a) When the gutter is full, what is the rate of draining? (b) The gutter is designed for a sudden rainstorm of up to 5 mm per hour. For this condition, what is the maximum roof area that can be drained successfully? (c) What is Red? P6.21 Water Tinyland governors mansion 20 cm

A steady push on the piston in Fig. P6.22 causes a fl ow rate Q 5 0.15 cm3 /s through the needle. The fl uid has 5 900 kg/m3 and 5 0.002 kg/(m ? s). What force F is required to maintain the fl ow? 1.5 cm 3 cm Q F D1 = 0.25 mm D2 = 1 cm

SAE 10 oil at 208C fl ows in a vertical pipe of diameter 2.5 cm. It is found that the pressure is constant throughout the fl uid. What is the oil fl ow rate in m3 /h? Is the fl ow up or down?

Two tanks of water at 208C are connected by a capillary tube 4 mm in diameter and 3.5 m long. The surface of tank 1 is 30 cm higher than the surface of tank 2. (a) Estimate the fl ow rate in m3 /h. Is the fl ow laminar? (b) For what tube diameter will Red be 500?

For the confi guration shown in Fig. P6.25, the fl uid is ethyl alcohol at 208C, and the tanks are very wide. Find the fl ow rate which occurs in m3 /h. Is the fl ow laminar? P6.25 2 mm 1 m 50 cm 40 cm 80 cm

Two oil tanks are connected by two 9-m-long pipes, as in Fig. P6.26. Pipe 1 is 5 cm in diameter and is 6 m higher than pipe 2. It is found that the fl ow rate in pipe 2 is twice as large as the fl ow in pipe 1. (a) What is the diameter of pipe 2? (b) Are both pipe fl ows laminar? (c) What is the fl ow rate in pipe 2 (m3 /s)? Neglect minor losses. Problems 425 SAE 30 W oil at 20C za = 22 m D1 = 5 cm D2 L = 9 m zb = 15 m 6 m

Let us attack Prob. P6.25 in symbolic fashion, using Fig. P6.27. All parameters are constant except the upper tank depth Z(t). Find an expression for the fl ow rate Q(t) as a function of Z(t). Set up a differential equation, and solve for the time t0 to drain the upper tank completely. Assume quasi-steady laminar fl ow. P6.27 , D Z(t) H d h L

For straightening and smoothing an airfl ow in a 50-cmdiameter duct, the duct is packed with a honeycomb of thin straws of length 30 cm and diameter 4 mm, as in Fig. P6.28. The inlet fl ow is air at 110 kPa and 208C, moving at an average velocity of 6 m/s. Estimate the pressure drop across the honeycomb. P6.28 6 m/s Thousands of straws 50 cm 30 cm

SAE 30W oil at 208C fl ows through a straight pipe 25 m long, with diameter 4 cm. The average velocity is 2 m/s. (a) Is the fl ow laminar? Calculate (b) the pressure drop and (c) the power required. (d) If the pipe diameter is doubled, for the same average velocity, by what percent does the

SAE 10 oil at 208C fl ows through the 4-cm-diameter vertical pipe of Fig. P6.30. For the mercury manometer reading h 5 42 cm shown, (a) calculate the volume fl ow rate in m3 /h and (b) state the direction of fl ow. P6.30 SAE 10 oil Mercury 3 m D = 4 cm 42 cm

A laminar fl ow element (LFE) (Meriam Instrument Co.) measures low gas-fl ow rates with a bundle of capillary tubes or ducts packed inside a large outer tube. Consider oxygen at 208C and 1 atm fl owing at 84 ft3 /min in a 4-indiameter pipe. (a) Is the fl ow turbulent when approaching the element? (b) If there are 1000 capillary tubes, L 5 4 in, select a tube diameter to keep Red below 1500 and also to keep the tube pressure drop no greater than 0.5 lbf/in2 . (c) Do the tubes selected in part (b) fi t nicely within the approach pipe?

SAE 30 oil at 208C fl ows in the 3-cm-diameter pipe in Fig. P6.32, which slopes at 378. For the pressure measurements shown, determine (a) whether the fl ow is up or down and (b) the fl ow rate in m3 /h. P6.32 pB = 180 kPa 37 pA = 500 kPa 1

Water at 208C is pumped from a reservoir through a vertical tube 10 ft long and 1/16th in in diameter. The pump provides a pressure rise of 11 lbf/in2 to the fl ow. Neglect entrance losses. (a) Calculate the exit velocity. (b) Approximately how high will the exit water jet rise? (c) Verify that the fl ow is laminar.

Derive the time-averaged x-momentum equation (6.21) by direct substitution of Eqs. (6.19) into the momentum equation (6.14). It is convenient to write the convective acceleration as du dt 5 0 0x (u2 ) 1 0 0y (uv) 1 0 0z (uw) which is valid because of the continuity relation, Eq. (6.14

In the overlap layer of Fig. 6.9a, turbulent shear is large. If we neglect viscosity, we can replace Eq. (6.24) with the approximate velocity-gradient function du dy 5 fcn(y, w, ) Show by dimensional analysis that this leads to the logarithmic overlap relation (6.28)

The following turbulent fl ow velocity data u(y), for air at 758F and 1 atm near a smooth fl at wall were taken in the University of Rhode Island wind tunnel: y, in 0.025 0.035 0.047 0.055 0.065 u, ft/s 51.2 54.2 56.8 57.6 59.1

Two infi nite plates a distance h apart are parallel to the xz plane with the upper plate moving at speed V, as in Fig. P6.37. There is a fl uid of viscosity and constant pressure between the plates. Neglecting gravity and assuming incompressible turbulent fl ow u(y) between the plates, use the logarithmic law and appropriate boundary conditions to derive a formula for dimensionless wall shear stress versus dimensionless plate velocity. Sketch a typical shape of the profi le u(y). P6.37 x y V h Fixed u

Suppose in Fig. P6.37 that h 5 3 cm, the fl uid in water at 208C, and the fl ow is turbulent, so that the logarithmic law is valid. If the shear stress in the fl uid is 15 Pa, what is V in m/s?

By analogy with laminar shear, 5 du/dy, T. V. Boussinesq in 1877 postulated that turbulent shear could also be related to the mean velocity gradient turb 5 du/dy, where is called the eddy viscosity and is much larger than . If the logarithmic overlap law, Eq. (6.28), is valid with turb < w, show that < u*y.

Theodore von Krmn in 1930 theorized that turbulent shear could be represented by turb 5 du/dy, where 5 2 y2 |du/dy| is called the mixing-length eddy viscosity and < 0.41 is Krmns dimensionless mixing-length constant [2, 3]. Assuming that turb < w near the wall, show that this expression can be integrated to yield the logarithmic overlap law, Eq. (6.28).

Two reservoirs, which differ in surface elevation by 40 m, are connected by 350 m of new pipe of diameter 8 cm. If the desired fl ow rate is at least 130 N/s of water at 208C, can the pipe material be made of (a) galvanized iron, (b) commercial steel, or (c) cast iron? Neglect minor losses

Fluid fl ows steadily, at volume rate Q, through a large horizontal pipe and then divides into two small pipes, the larger of which has an inside diameter of 25 mm and carries three times the fl ow of the smaller pipe. Both small pipes have the same length and pressure drop. If all fl ows are turbulent, at ReD near 104 , estimate the diameter of the smaller pipe.

A reservoir supplies water through 100 m of 30-cm-diameter cast iron pipe to a turbine that extracts 80 hp from the fl ow. The water then exhausts to the atmosphere. P6.43 Water at 20C Turbine Cast iron pipe z1 = 35 m z2 = 5 m

Mercury at 208C fl ows through 4 m of 7-mm-diameter glass tubing at an average velocity of 5 m/s. Estimate the head loss in m and the pressure drop in kPa

Oil, SG 5 0.88 and 5 4 E-5 m2 /s, fl ows at 400 gal/min through a 6-in asphalted cast iron pipe. The pipe is 0.5 mi long and slopes upward at 88 in the fl ow direction. Compute the head loss in ft and the pressure change

The Keystone Pipeline in the chapter opener photo has a diameter of 36 inches and a design fl ow rate of 590,000 barrels per day of crude oil at 408C. If the pipe material is new steel, estimate the pump horsepower required per mile of pipe.

The gutter and smooth drainpipe in Fig. P6.47 remove rainwater from the roof of a building. The smooth drainpipe is 7 cm in diameter. (a) When the gutter is full, estimate the rate of draining. (b) The gutter is designed for a sudden rainstorm of up to 5 inches per hour. For this condition, what is the maximum roof area that can be drained successfully? P6.47 Water 4.2 m

Follow up Prob. P6.46 with the following question. If the total Keystone pipeline length, from Alberta to Texas, is 2147 miles, how much fl ow, in barrels per minute, will result if the total available pumping power is 8,000 hp?

The tankpipe system of Fig. P6.49 is to deliver at least 11 m3 /h of water at 208C to the reservoir. What is the maximum roughness height allowable for the pipe? L = 5 m, d = 3 cm 4 m 2 m Water at 20C

Ethanol at 208C fl ows at 125 U.S. gal/min through a horizontal cast iron pipe with L 5 12 m and d 5 5 cm. Neglecting entrance effects, estimate (a) the pressure gradient dp/dx, (b) the wall shear stress w, and (c) the percentage reduction in friction factor if the pipe walls are polished to a smooth surface.

The viscous sublayer (Fig. 6.9) is normally less than 1 percent of the pipe diameter and therefore very diffi cult to probe with a fi nite-sized instrument. In an effort to generate a thick sublayer for probing, Pennsylvania State University in 1964 built a pipe with a fl ow of glycerin. Assume a smooth 12-in-diameter pipe with V 5 60 ft/s and glycerin at 208C. Compute the sublayer thickness in inches and the pumping horsepower required at 75 percent effi ciency if L 5 40 ft.

The pipe fl ow in Fig. P6.52 is driven by pressurized air in the tank. What gage pressure p1 is needed to provide a 208C water fl ow rate Q 5 60 m3 /h? P6.52 30 m 60 m 80 m 10 m Smooth pipe: d = 5 cm Q Open jet p1

Water at 208C fl ows by gravity through a smooth pipe from one reservoir to a lower one. The elevation difference is 60 m. The pipe is 360 m long, with a diameter of 12 cm. Calculate the expected fl ow rate in m3 /h. Neglect minor losses.

A swimming pool W by Y by h deep is to be emptied by gravity through the long pipe shown in Fig. P6.54. Assuming an average pipe friction factor fav and neglecting minor losses, derive a formula for the time to empty the tank from an initial level ho. h Water Bottom = W by Y Pipe: L, D,  V

The reservoirs in Fig. P6.55 contain water at 208C. If the pipe is smooth with L 5 4500 m and d 5 4 cm, what will the fl ow rate in m3 /h be for Dz 5 100 m? P6.55 1 2 B L, D, z

The Alaska Pipeline in the chapter opener photo has a design fl ow rate of 4.4 E7 gallons per day of crude oil at 608C (see Fig. A.1). (a) Assuming a galvanized-iron wall, estimate the total pressure drop required for the 800-mile trip. (b) If there are nine equally spaced pumps, estimate the horsepower each pump must deliver

Apply the analysis of Prob. P6.54 to the following data. Let W 5 5 m, Y 5 8 m, ho 5 2 m, L 5 15 m, D 5 5 cm, and 5 0. (a) By letting h 5 1.5 m and 0.5 m as representative depths, estimate the average friction factor. Then (b) estimate the time to drain the pool

For the system in Prob. 6.53, a pump is used at night to drive water back to the upper reservoir. If the pump delivers 15,000 W to the water, estimate the fl ow rate

The following data were obtained for fl ow of 208C water at 20 m3 /h through a badly corroded 5-cm-diameter pipe that slopes downward at an angle of 88: p1 5 420 kPa, z1 5 12 m, p2 5 250 kPa, z2 5 3 m. Estimate (a) the roughness ratio of the pipe and (b) the percentage change in head loss if the pipe were smooth and the fl ow rate the same

In the spirit of Haalands explicit pipe friction factor approximation, Eq. (6.49), Jeppson [20] proposed the following explicit formula: 1 1f < 22.0 log10 a /d 3.7 1 5.74 Re0.9 d b (a) Is this identical to Haalands formula with just a simple rearrangement? Explain. (b) Compare Jeppsons formula to Haalands for a few representative values of (turbulent) Red and /d and their errors compared to the Colebrook formula (6.48). Discuss briefl y

What level h must be maintained in Fig. P6.61 to deliver a fl ow rate of 0.015 ft3 /s through the 1 2-in commercial steel pipe? P6.61 Water at 20C h L = 80 ft D = 1 2 in

Water at 208C is to be pumped through 2000 ft of pipe from reservoir 1 to 2 at a rate of 3 ft3 /s, as shown in Fig. P6.62. If the pipe is cast iron of diameter 6 in and the pump is 75 percent effi cient, what horsepower pump is needed? P6.62 Pump L = 2000 ft 2 1 120 ft

A tank contains 1 m3 of water at 208C and has a drawncapillary outlet tube at the bottom, as in Fig. P6.63. Find the outlet volume fl ux Q in m3 /h at this instant.

For the system in Fig. P6.63, solve for the fl ow rate in m3 /h if the fl uid is SAE 10 oil at 208C. Is the fl ow laminar or turbulent?

In Prob. P6.63 the initial fl ow is turbulent. As the water drains out of the tank, will the fl ow revert to laminar motion as the tank becomes nearly empty? If so, at what tank depth? Estimate the time, in h, to drain the tank completely

Ethyl alcohol at 208C fl ows through a 10-cm horizontal drawn tube 100 m long. The fully developed wall shear stress is 14 Pa. Estimate (a) the pressure drop, (b) the volume fl ow rate, and (c) the velocity u at r 5 1 cm.

A straight 10-cm commercial-steel pipe is 1 km long and is laid on a constant slope of 58. Water at 208C fl ows downward, due to gravity only. Estimate the fl ow rate in m3 /h. What happens if the pipe length is 2 km?

The Moody chart cannot fi nd V directly, since V appears in both ordinate and abscissa. (a) Arrange the variables (hf , d, g, L, ) into a single dimensionless group, with hf d3 in the numerator, denoted as , which equals (f Red 2 /2). (b) Rearrange the Colebrook formula (6.48) to solve for Red in terms of . (c) For extra credit, solve Example 6.9 with this new formula.

9 For Prob. P6.62 suppose the only pump available can deliver 80 hp to the fl uid. What is the proper pipe size in inches to maintain the 3 ft3 /s fl ow rate?

Ethylene glycol at 208C fl ows through 80 m of cast iron pipe of diameter 6 cm. The measured pressure drop is 250 kPa. Neglect minor losses. Using a noniterative formulation, estimate the fl ow rate in m3 /h.

It is desired to solve Prob. 6.62 for the most economical pump and cast iron pipe system. If the pump costs $125 per horsepower delivered to the fl uid and the pipe costs $7000 per inch of diameter, what are the minimum cost and the pipe and pump size to maintain the 3 ft3 /s fl ow rate? Make some simplifying assumptions.

Modify Prob. P6.57 by letting the diameter be unknown. Find the proper pipe diameter for which the pool will drain in about two hours fl at.

For 208C water fl ow in a smooth, horizontal 10-cm pipe, with Dp/L 5 1000 Pa/m, the writer computed a fl ow rate of 0.030 m3 /s. (a) Verify, or disprove, the writers answer. (b) If verifi ed, use the power-law friction factor relation, Eq. (6.41), to estimate the pipe diameter that will triple this fl ow rate. (c) For extra credit, use the more exact friction factor relation, Eq. (6.38), to solve part (b).

Two reservoirs, which differ in surface elevation by 40 m, are connected by a new commercial steel pipe of diameter 8 cm. If the desired fl ow rate is 200 N/s of water at 208C, what is the proper length of the pipe?

You wish to water your garden with 100 ft of 5 8-in-diameter hose whose roughness is 0.011 in. What will be the delivery, in ft3 /s, if the gage pressure at the faucet is 60 lbf/in2 ? If there is no nozzle (just an open hose exit), what is the maximum horizontal distance the exit jet will carry?

The small turbine in Fig. P6.76 extracts 400 W of power from the water fl ow. Both pipes are wrought iron. Compute the fl ow rate Q in m3 /h. Why are there two solutions? Which is better? Q Water 20C Turbine 30 m D = 4 cm 10 m D = 6 cm 20 m

Modify Prob. P6.76 into an economic analysis, as follows: Let the 40 m of wrought iron pipe have a uniform diameter d. Let the steady water fl ow available be Q 5 30 m3 /h. The cost of the turbine is $4 per watt developed, and the cost of the piping is $75 per centimeter of diameter. The power generated may be sold for $0.08 per kilowatt-hour. Find the proper pipe diameter for minimum payback timethat is, the minimum time for which the power sales will equal the initial cost of the system.

In Fig. P6.78 the connecting pipe is commercial steel 6 cm in diameter. Estimate the fl ow rate, in m3 /h, if the fl uid is water at 208C. Which way is the fl ow?

A garden hose is to be used as the return line in a waterfall display at a mall. In order to select the proper pump, you need to know the roughness height inside the garden hose. Unfortunately, roughness information is not supplied by the hose manufacturer. So you devise a simple experiment

The head-versus-fl ow-rate characteristics of a centrifugal pump are shown in Fig. P6.80. If this pump drives water at 208C through 120 m of 30-cm-diameter cast iron pipe, what will be the resulting fl ow rate, in m3 /s? P6.80 80 m hp 0 Pump performance Parabola Q 2m3/s

The pump in Fig. P6.80 is used to deliver gasoline at 208C through 350 m of 30-cm-diameter galvanized iron pipe. Estimate the resulting fl ow rate, in m3 /s. (Note that the pump head is now in meters of gasoline.)

Fluid at 208C fl ows through a horizontal galvanized-iron pipe 20 m long and 8 cm in diameter. The wall shear stress is 90 Pa. Calculate the fl ow rate in m3 /h if the fl uid is (a) glycerin and (b) water

For the system of Fig. P6.55, let Dz 5 80 m and L 5 185 m of cast iron pipe. What is the pipe diameter for which the fl ow rate will be 7 m3 /h?

It is desired to deliver 60 m3 /h of water at 208C through a horizontal asphalted cast iron pipe. Estimate the pipe diameter that will cause the pressure drop to be exactly 40 kPa per 100 m of pipe length

For the system in Prob. P6.53, a pump, which delivers 15,000 W to the water, is used at night to refi ll the upper reservoir. The pipe diameter is increased from 12 cm to provide more fl ow. If the resultant fl ow rate is 90 m3 /h, estimate the new pipe siz

SAE 10 oil at 208C fl ows at an average velocity of 2 m/s between two smooth parallel horizontal plates 3 cm apart. Estimate (a) the centerline velocity, (b) the head loss per meter, and (c) the pressure drop per meter.

A commercial steel annulus 40 ft long, with a 5 1 in and b 5 1 2 in, connects two reservoirs that differ in surface height by 20 ft. Compute the fl ow rate in ft3 /s through the annulus if the fl uid is water at 208C.

An oil cooler consists of multiple parallel-plate passages, as shown in Fig. P6.88. The available pressure drop is 6 kPa, and the fl uid is SAE 10W oil at 208C. If the desired total fl ow rate is 900 m3 /h, estimate the appropriate number of passages. The plate walls are hydraulically smooth. 2 m 50 cm 50 cm Flow

An annulus of narrow clearance causes a very large pressure drop and is useful as an accurate measurement of viscosity. If a smooth annulus 1 m long with a 5 50 mm and b 5 49 mm carries an oil flow at 0.001 m3 /s, what is the oil viscosity if the pressure drop is 250 kPa?

A rectangular sheet-metal duct is 200 ft long and has a fi xed height H 5 6 in. The width B, however, may vary from 6 to 36 in. A blower provides a pressure drop of 80 Pa of air at 208C and 1 atm. What is the optimum width B that will provide the most airfl ow in ft3 /s?

Heat exchangers often consist of many triangular passages. Typical is Fig. P6.91, with L 5 60 cm and an isosceles-triangle cross section of side length a 5 2 cm and included angle 5 808. If the average velocity is V 5 2 m/s and the fl uid is SAE 10 oil at 208C, estimate the pressure drop.

A large room uses a fan to draw in atmospheric air at 208C through a 30-cm by 30-cm commercial-steel duct 12 m long, as in Fig. P6.92. Estimate (a) the airfl ow rate in m3 /h if the room pressure is 10 Pa vacuum and (b) the room pressure if the fl ow rate is 1200 m3 /h. Neglect minor losses. 12 m Room 30 cm by 30 cm patm Fan P6.92

In Moodys Example 6.6, the 6-inch diameter, 200-ft-long asphalted cast iron pipe has a pressure drop of about 280 lbf/ft2 when the average water velocity is 6 ft/s. Compare this to an annular cast iron pipe with an inner diameter of 6 in and the same annular average velocity of 6 ft/s. (a) What outer diameter would cause the fl ow to have the same pressure drop of 280 lbf/ft2 ? (b) How do the crosssection areas compare, and why? Use the hydraulic diameter approximation.

Air at 208C fl ows through a smooth duct of diameter 20 cm at an average velocity of 5 m/s. It then fl ows into a smooth square duct of side length a. Find the square duct size a for which the pressure drop per meter will be exactly the same as the circular duct

Although analytical solutions are available for laminar fl ow in many duct shapes [34], what do we do about ducts of arbitrary shape? Bahrami et al. [57] propose that a better approach to the pipe result, f Re 5 64, is achieved by replacing the hydraulic diameter Dh with 1A, where A is the area of the cross section. Test this idea for the isosceles triangles of Table 6.4. If time is short, at least try 108, 508, and 808. What do you conclude about this idea?

A fuel cell [59] consists of air (or oxygen) and hydrogen micro ducts, separated by a membrane that promotes proton exchange for an electric current, as in Fig. P6.96. Suppose that the air side, at 208C and approximately 1 atm, has fi ve 1 mm by 1 mm ducts, each 1 m long. The total fl ow rate is 1.5 E-4 kg/s. (a) Determine if the fl ow is laminar or turbulent. (b) Estimate the pressure drop. (Problem courtesy of Dr. Pezhman Shirvanian.) P6.96 Anode Cathode 1 mm by 1 mm by 1m PEM membrane

A heat exchanger consists of multiple parallel-plate passages, as shown in Fig. P6.97. The available pressure drop is 2 kPa, and the fl uid is water at 208C. If the desired total fl ow rate is 900 m3 /h, estimate the appropriate number of passages. The plate walls are hydraulically smooth. 2 m 50 cm 50 cm Flow

A rectangular heat exchanger is to be divided into smaller sections using sheets of commercial steel 0.4 mm thick, as sketched in Fig. P6.98. The fl ow rate is 20 kg/s of water at 208C. Basic dimensions are L 5 1 m, W 5 20 cm, and H 5 10 cm. What is the proper number of square sections if the overall pressure drop is to be no more than 1600 Pa? 432 Chapter 6 Viscous Flow in Ducts P6.98 H W

In Sec. 6.11 it was mentioned that Roman aqueduct customers obtained extra water by attaching a diffuser to their pipe exits. Fig. P6.99 shows a simulation: a smooth inlet pipe, with or without a 158 conical diffuser expanding to a 5-cm-diameter exit. The pipe entrance is sharp-edged. Calculate the fl ow rate (a) without and (b) with the diffuser. D2 = 5 cm 15 diffuser

Modify Prob. P6.55 as follows: Assume a pump can deliver 3 kW to pump the water back up to reservoir 1 from reservoir 2. Accounting for an open fl anged globe valve and sharp-edged entrance and exit, estimate the predicted fl ow rate, in m3 /h.

In Fig. P6.101 a thick fi lter is being tested for losses. The fl ow rate in the pipe is 7 m3 /min, and the upstream pressure is 120 kPa. The fl uid is air at 208C. Using the water manometer reading, estimate the loss coeffi cient K of the fi lter. P6.101 4 cm Water Air d = 10 cm

2 A 70 percent effi cient pump delivers water at 208C from one reservoir to another 20 ft higher, as in Fig. P6.102. The piping system consists of 60 ft of galvanized iron 2-in pipe, a reentrant entrance, two screwed 908 long-radius elbows, a screwed-open gate valve, and a sharp exit. What is the input power required in horsepower with and without a 68 well-designed conical expansion added to the exit? The fl ow rate is 0.4 ft3 /s. 20 ft 6 cone Pump

The reservoirs in Fig. P6.103 are connected by cast iron pipes joined abruptly, with sharp-edged entrance and exit. Including minor losses, estimate the fl ow of water at 208C if the surface of reservoir 1 is 45 ft higher than that of reservoir 2. 1 2 D = 2 in L = 20 ft D = 1 in L = 20 ft 1 in 2 in P6.103

Consider a 208C fl ow at 2 m/s through a smooth 3-mm diameter microtube which consists of a straight run of 10 cm, a long radius bend, and another straight run of 10 cm. Compute the total pressure drop if the fl uid is (a) water; and (b) ethylene glycol

The system in Fig. P6.105 consists of 1200 m of 5 cm cast iron pipe, two 458 and four 908 fl anged long-radius elbows, a fully open fl anged globe valve, and a sharp exit into a reservoir. If the elevation at point 1 is 400 m, what gage pressure is required at point 1 to deliver 0.005 m3 /s of water at 208C into the reservoir? Problems 433 1 Elevation 500 m Sharp exit Open globe 45 45

The water pipe in Fig. P6.106 slopes upward at 308. The pipe has a 1-in diameter and is smooth. The fl anged globe valve is fully open. If the mercury manometer shows a 7-in defl ection, what is the fl ow rate in ft3 /s? P6.106 7 in 10 ft Mercury Globe

A tank of water 4 m in diameter and 7 m deep is to be drained by a 5-cm-diameter exit pipe at the bottom, as in Fig. P6.107. In design (1), the pipe extends out for 1 m and into the tank for 10 cm. In design (2), the interior pipe is removed and the entrance beveled, Fig. 6.21, so that K < 0.1 in the entrance. (a) An engineer claims that design (2) will drain 25 percent faster than design (1). Is this claim true? (b) Estimate the time to drain of design (2), assuming f < 0.020. (1) (2)

The water pump in Fig. P6.108 maintains a pressure of 6.5 psig at point 1. There is a fi lter, a half-open disk valve, and two regular screwed elbows. There are 80 ft of 4-in diameter commercial steel pipe. (a) If the fl ow rate is 0.4 ft3 /s, what is the loss coeffi cient of the fi lter? (b) If the disk valve is wide open and Kfi lter 5 7, what is the resulting fl ow rate? 1 Pump Valve Filter Elbows 9 ft

In Fig. P6.109 there are 125 ft of 2-in pipe, 75 ft of 6-in pipe, and 150 ft of 3-in pipe, all cast iron. There are three 908 elbows and an open globe valve, all fl anged. If the exit elevation is zero, what horsepower is extracted by the turbine when the fl ow rate is 0.16 ft3 /s of water at 208C? Open globe Turbine 3 in 6 in 2 in Elevation 100 ft

In Fig. P6.110 the pipe entrance is sharp-edged. If the fl ow rate is 0.004 m3 /s, what power, in W, is extracted by the turbine? Water 40 m Turbine Open globe valve Cast iron: L = 125 m, D = 5 cm

For the parallel-pipe system of Fig. P6.111, each pipe is cast iron, and the pressure drop p1 2 p2 5 3 lbf/in2 . Compute the total fl ow rate between 1 and 2 if the fl uid is SAE 10 oil at 208C. 434 Chapter 6 Viscous Flow in Ducts L = 200 ft 1 2

If the two pipes in Fig. P6.111 are instead laid in series with the same total pressure drop of 3 lbf/in2 , what will the fl ow rate be? The fl uid is SAE 10 oil at 208C

The parallel galvanized iron pipe system of Fig. P6.113 delivers water at 208C with a total fl ow rate of 0.036 m3 /s. If the pump is wide open and not running, with a loss coeffi cient K 5 1.5, determine (a) the fl ow rate in each pipe and (b) the overall pressure drop. L1 = 60 m, D1 = 5 cm Q = 0.036 m3/s L2 = 55 m, D2 = 4 cm

A blower supplies standard air to a plenum that feeds two horizontal square sheet-metal ducts with sharp-edged entrances. One duct is 100 ft long, with a cross-section 6 in by 6 in. The second duct is 200 ft long. Each duct exhausts to the atmosphere. When the plenum pressure is 5.0 lbf/ft2 (gage) the volume fl ow in the longer duct is three times the fl ow in the shorter duct. Estimate both volume fl ows and the cross-section size of the longer duct.

In Fig. P6.115 all pipes are 8-cm-diameter cast iron. Determine the fl ow rate from reservoir 1 if valve C is (a) closed and (b) open, K 5 0.5

For the series-parallel system of Fig. P6.116, all pipes are 8-cm-diameter asphalted cast iron. If the total pressure drop p1 2 p2 5 750 kPa, fi nd the resulting fl ow rate Q m3 /h for water at 208C. Neglect minor losses

A blower delivers air at 3000 m3 /h to the duct circuit in Fig. P6.117. Each duct is commercial steel and of square cross section, with side lengths a1 5 a3 5 20 cm and a2 5 a4 5 12 cm. Assuming sea-level air conditions, estimate the power required if the blower has an effi ciency of 75 percent. Neglect minor losses.

For the piping system of Fig. P6.118, all pipes are concrete with a roughness of 0.04 in. Neglecting minor losses, compute the overall pressure drop p1 2 p2 in lbf/in2 if Q 520 ft3 /s. The fl uid is water at 208C. D = 8 in L = 1500 ft 1 2 L = 1000 ft D = 12 in D = 15 in L = 1200 ft

For the piping system of Prob. P6.111, let the fl uid be gasoline at 208C, with both pipes cast iron. If the fl ow rate in the 2-in pipe (b) is 1.2 ft3 /min, estimate the fl ow rate in the 3-in pipe (a), in ft3 /min

Three cast iron pipes are laid in parallel with these dimensions: Pipe Length, m Diameter, cm 1 800 12 2 600 8 3 900 10 The total fl ow rate is 200 m3 /h of water at 208C. Determine (a) the fl ow rate in each pipe and (b) the pressure drop across the system

Consider the three-reservoir system of Fig. P6.121 with the following data: L1 5 95m L2 5 125 m L3 5 160 m z1 5 25 m z2 5 115 m z3 5 85 m All pipes are 28-cm-diameter unfi nished concrete ( 5 1 mm). Compute the steady fl ow rate in all pipes for water at 208C. Z1 Z2 Z3 L1 L2 L3

Modify Prob. P6.121 as follows: Reduce the diameter to 15 cm (with 5 1 mm), and compute the fl ow rates for water at 208C. These fl ow rates distribute in nearly the same manner as in Prob. P6.121 but are about 5.2 times lower. Can you explain this difference?

Modify Prob. P6.121 as follows: All data are the same except that z3 is unknown. Find the value of z3 for which the fl ow rate in pipe 3 is 0.2 m3 /s toward the junction. (This problem requires iteration and is best suited to a computer.)

The three-reservoir system in Fig. P6.124 delivers water at 208C. The system data are as follows: D1 5 8 in D2 5 6 in D3 5 9 in L1 5 1800 ft L2 5 1200 ft L3 5 1600 ft All pipes are galvanized iron. Compute the fl ow rate in all pipes. P6.124 1 2 3 z1 = 20 ft z2 = 100 ft z3 = 50 ft

Suppose that the three cast iron pipes in Prob. P6.120 are instead connected to meet smoothly at a point B, as shown in Fig. P6.125. The inlet pressures in each pipe are p1 5 200 kPa p2 5 160 kPa p3 5 100 kPa. The fl uid is water at 208C. Neglect minor losses. Estimate the fl ow rate in each pipe and whether it is toward or away from point B. B 1 2 3

Modify Prob. P6.124 as follows: Let all data be the same except that pipe 1 is fi tted with a butterfl y valve (Fig. 6.19b). Estimate the proper valve opening angle (in degrees) for the fl ow rate through pipe 1 to be reduced to 1.5 ft3 /s toward reservoir 1. (This problem requires iteration and is best suited to a computer.)

In the fi ve-pipe horizontal network of Fig. P6.127, assume that all pipes have a friction factor f 5 0.025. For the given inlet and exit fl ow rate of 2 ft3 /s of water at 436 Chapter 6 Viscous Flow in Ducts 208C, determine the fl ow rate and direction in all pipes. If pA 5 120 lbf/in2 gage, determine the pressures at points B, C, and D. d = 8 in D A B 4000 ft 3000 ft 2 ft3/s 2 ft3/s 9 in 3 in C 6 in 8 in

Modify Prob. P6.127 as follows: Let the inlet fl ow rate at A and the exit fl ow at D be unknown. Let pA 2 pB 5 100 lbf/in2 . Compute the fl ow rate in all fi ve pipes.

In Fig. P6.129 all four horizontal cast iron pipes are 45 m long and 8 cm in diameter and meet at junction a, delivering water at 208C. The pressures are known at four points as shown: p1 5 950 kPa p2 5 350 kPa p3 5 675 kPa p4 5 100 kPa Neglecting minor losses, determine the fl ow rate in each pipe. P6.129 p1 L1 p2 L2 L3 a L4 p4 p3 P6.130 In Fig. P6.130 lengths AB and BD are 2000

In Fig. P6.130 lengths AB and BD are 2000 and 1500 ft, respectively. The friction factor is 0.022 everywhere, and pA 5 90 lbf/in2 gage. All pipes have a diameter of 6 in. For water at 208C, determine the fl ow rate in all pipes and the pressures at points B, C, and D. C D A B 0.5 ft3/s 2.0 ft3/s 0.5 ft3 /s 1.0 ft3/s

A water tunnel test section has a 1-m diameter and fl ow properties V 5 20 m/s, p 5 100 kPa, and T 5 208C. The boundary layer blockage at the end of the section is 9 percent. If a conical diffuser is to be added at the end of the section to achieve maximum pressure recovery, what should its angle, length, exit diameter, and exit pressure be?

For Prob. P6.131 suppose we are limited by space to a total diffuser length of 10 m. What should the diffuser angle, exit diameter, and exit pressure be for maximum recovery?

A wind tunnel test section is 3 ft square with fl ow properties V 5 150 ft/s, p 5 15 lbf/in2 absolute, and T 5 688F. Boundary layer blockage at the end of the test section is 8 percent. Find the angle, length, exit height, and exit pressure of a fl at-walled diffuser added onto the section to achieve maximum pressure recovery.

4 For Prob. P6.133 suppose we are limited by space to a total diffuser length of 30 ft. What should the diffuser angle, exit height, and exit pressure be for maximum recovery?

An airplane uses a pitot-static tube as a velocimeter. The measurements, with their uncertainties, are a static temperature of (211 6 3)8C, a static pressure of 60 6 2 kPa, and a pressure difference (po 2 ps) 5 3200 6 60 Pa. (a) Estimate the airplanes velocity and its uncertainty. (b) Is a compressibility correction needed?

For the pitot-static pressure arrangement of Fig. P6.136, the manometer fl uid is (colored) water at 208C. Estimate (a) the centerline velocity, (b) the pipe volume fl ow, and (c) the (smooth) wall shear stress.

For the 208C water fl ow of Fig. P6.137, use the pitot-static arrangement to estimate (a) the centerline velocity and (b) the volume fl ow in the 5-in-diameter smooth pipe. (c) What error in fl ow rate is caused by neglecting the 1-ft elevation difference?

An engineer who took college fl uid mechanics on a passfail basis has placed the static pressure hole far upstream of the stagnation probe, as in Fig. P6.138, thus contaminating the pitot measurement ridiculously with pipe friction losses. If the pipe fl ow is air at 208C and 1 atm and the manometer fl uid is Meriam red oil (SG 5 0.827), estimate the air centerline velocity for the given manometer reading of 16 cm. Assume a smooth-walled tube. P6.138 D = 6 cm 16 cm 10 m Air

9 Professor Walter Tunnel needs to measure the fl ow velocity in a water tunnel. Due to budgetary restrictions, he cannot afford a pitot-static probe, but instead inserts a total head probe and a static pressure probe, as shown in Fig. P6.139, a distance h1 apart from each other. Both probes are in the main free stream of the water tunnel, unaffected by the thin boundary layers on the sidewalls. The two probes are connected as shown to a U-tube manometer. The densities and vertical distances are shown in Fig. P6.139. (a) Write an expression for velocity V in terms of the parameters in the problem. (b) Is it critical that distance h1 be measured accurately? (c) How does the expression for velocity V differ from that which would be obtained if a pitot-static probe had been available and used with the same U-tube manometer? h1 h2 h3 U-tube manometer ptotal pstatic w m V P6.139

0 Gasoline at 208C fl ows at 3 m3 /h in a 6-cm-diameter pipe. A 4-cm-diameter thin-plate orifi ce with corner taps is installed. Estimate the measured pressure drop, in Pa.

Gasoline at 208C flows at 105 m3 /h in a 10-cm-diameter pipe. We wish to meter the flow with a thin-plate orifice and a differential pressure transducer that reads best at about 55 kPa. What is the proper ratio for the orifice?

The shower head in Fig. P6.142 delivers water at 508C. An orifi ce-type fl ow reducer is to be installed. The upstream pressure is constant at 400 kPa. What fl ow rate, in gal/min, results without the reducer? What reducer orifi ce diameter would decrease the fl ow by 40 percent?

A 10-cm-diameter smooth pipe contains an orifi ce plate with D: 1 2D taps and 5 0.5. The measured orifi ce pressure drop is 75 kPa for water fl ow at 208C. Estimate the fl ow rate, in m3 /h. What is the nonrecoverable head loss?

Water at 208C fl ows through the orifi ce in Fig. P6.154, which is monitored by a mercury manometer. If d 5 3 cm, (a) what is h when the fl ow rate is 20 m3 /h and (b) what is Q in m3 /h when h 5 58 cm? Water d h 5 cm Mercury

The 1-m-diameter tank in Fig. P6.145 is initially fi lled with gasoline at 208C. There is a 2-cm-diameter orifi ce in the bottom. If the orifi ce is suddenly opened, estimate the time for the fl uid level h(t) to drop from 2.0 to 1.6 m. P6.145 1 m h(0) = 2 m Q(t) h(t)

A pipe connecting two reservoirs, as in Fig. P6.146, contains a thin-plate orifi ce. For water fl ow at 208C, estimate (a) the volume fl ow through the pipe and (b) the pressure drop across the orifi ce plate. P6.146 20 m 3-cm orifice L = 100 m D = 5 cm

Air fl ows through a 6-cm-diameter smooth pipe that has a 2-m-long perforated section containing 500 holes (diameter 1 mm), as in Fig. P6.147. Pressure outside the pipe is sea-level standard air. If p1 5 105 kPa and Q1 5 110 m3 /h, estimate p2 and Q2, assuming that the holes are approximated by thin-plate orifi ces. (Hint: A momentum control volume may be very useful.) D = 6 cm 2 m 500 holes (diameter 1 mm)

A smooth pipe containing ethanol at 208C fl ows at 7 m3 /h through a Bernoulli obstruction, as in Fig. P6.148. Three piezometer tubes are installed, as shown. If the obstruction is a thin-plate orifi ce, estimate the piezometer levels (a) h2 and (b) h3. D = 5 cm 5 m d = 3 cm h3 h2 h1= 1 m

In a laboratory experiment, air at 208C fl ows from a large tank through a 2-cm-diameter smooth pipe into a sea-level atmosphere, as in Fig. P6.149. The fl ow is metered by a long-radius nozzle of 1-cm diameter, using a manometer with Meriam red oil (SG 5 0.827). The pipe is 8 m long. The measurements of tank pressure and manometer height are as follows: ptank, Pa(gage): 60 320 1200 2050 2470 3500 4900 hmano, mm: 6 38 160 295 380 575 820 Use these data to calculate the fl ow rates Q and Reynolds numbers ReD and make a plot of measured fl ow rate versus tank pressure. Is the fl ow laminar or turbulent? Compare the data with theoretical results obtained from the Moody chart, including minor losses. Discuss. Air tank pgage pa = 1 atm 8 m h

Gasoline at 208C fl ows at 0.06 m3 /s through a 15-cm pipe and is metered by a 9-cm long-radius fl ow nozzle (Fig. 6.40a). What is the expected pressure drop across the nozzle?

An engineer needs to monitor a fl ow of 208C gasoline at about 250 6 25 gal/min through a 4-in-diameter smooth pipe. She can use an orifi ce plate, a long-radius fl ow nozzle, or a venturi nozzle, all with 2-in-diameter throats. The only differential pressure gage available is accurate in the range 6 to 10 lbf/in2 . Disregarding fl ow losses, which device is best?

Kerosene at 208C fl ows at 20 m3 /h in an 8-cm-diameter pipe. The fl ow is to be metered by an ISA 1932 fl ow nozzle so that the pressure drop is 7000 Pa. What is the proper nozzle diameter?

Two water tanks, each with base area of 1 ft2 , are connected by a 0.5-in-diameter long-radius nozzle as in Fig. P6.153. If h 5 1 ft as shown for t 5 0, estimate the time for h(t) to drop to 0.25 ft

Gasoline at 208C fl ows through a 6-cm-diameter pipe. It is metered by a modern venturi nozzle with d 5 4 cm. The measured pressure drop is 8.5 kPa. Estimate the fl ow rate in gallons per minute.

It is desired to meter methanol at 208C fl owing through a 5-in-diameter pipe. The expected fl ow rate is about 300 gal/min. Two fl owmeters are available: a venturi nozzle and a thinplate orifi ce, each with d 5 2 in. The differential pressure gage on hand is most accurate at about 1215 lbs/in2 . Which meter is better for this job?

Ethanol at 208C fl ows down through a modern venturi nozzle as in Fig. P6.156. If the mercury manometer reading is 4 in, as shown, estimate the fl ow rate, in gal/min. P6.156

Modify Prob. P6.156 if the fl uid is air at 208C, entering the venturi at a pressure of 18 lbf/in2 . Should a compressibility correction be used?

Water at 208C fl ows in a long horizontal commercial steel 6-cm-diameter pipe that contains a classical Herschel venturi with a 4-cm throat. The venturi is connected to a mercury manometer whose reading is h 5 40 cm. Estimate 440 Chapter 6 Viscous Flow in Ducts (a) the fl ow rate, in m3 /h, and (b) the total pressure difference between points 50 cm upstream and 50 cm downstream of the venturi

A modern venturi nozzle is tested in a laboratory fl ow with water at 208C. The pipe diameter is 5.5 cm, and the venturi throat diameter is 3.5 cm. The fl ow rate is measured by a weigh tank and the pressure drop by a watermercury manometer. The mass fl ow rate and manometer readings are as follows: m # , kg/s 0.95 1.98 2.99 5.06 8.15 h, mm 3.7 15.9 36.2 102.4 264.4 Use these data to plot a calibration curve of venturi discharge coeffi cient versus Reynolds number. Compare with the accepted correlation, Eq. (6.114).

An instrument popular in the water supply industry, sketched in Fig. P6.161, is the single jet water meter. (a) How does it work? (b) What do you think a typical calibration curve would look like? (c) Can you cite further details, for example, reliability, head loss, cost [58]?

An instrument popular in the water supply industry, sketched in Fig. P6.161, is the single jet water meter. (a) How does it work? (b) What do you think a typical calibration curve would look like? (c) Can you cite further details, for example, reliability, head loss, cost [58]?

Air fl ows at high speed through a Herschel venturi monitored by a mercury manometer, as shown in Fig. P6.162. The upstream conditions are 150 kPa and 808C. If h 5 37 cm, estimate the mass fl ow in kg/s. (Hint: The fl ow is compressible.)

Modify Prob. P6.162 as follows: Find the manometer reading h for which the mass fl ow through the venturi is approximately 0.4 kg/s. (Hint: The fl ow is compressible.)