Water from a test apparatus is diverted into a calibrated volumetric tank for 6 min. If

List five different instruments or approaches that engineers use to measure fluid velocity, and five more that arc used to measure pressure. For each instrument or approach, list two advantages and two disadvantages, using this text or sources on the internet.

Consider measuring the speed of an automobile by building a stagnation tube from a drinking straw and then using this device with a water-filled U-tube manometer. a. Make a sketch that illustrates how you would propose making this measurement. b. Determine the lowest velocity that could be measured. Assume that the lower limit is based on the resolution of the manometer.

Without exceeding an error of 2.5%, what is the mininmm air velocity that can be obtained using a 1 mm circular stagnation tube if the formula v = V2t:.p.,,8/p = V2gh,.ag is used for computing the velocity? Assume standard atmospheric conditions.

Without exceeding an error of I%, what is the minimum water velocity that can be obtained using a 1.5-mm circular stagnation tube if the formula v = Vit:.p.,.giP = V2gh,tg is used for computing the velocity? Assume the water temperature is 20C.

A stagnation tube 2 mm in diameter is used to measure the velocity in a stream of air as shown. What is the air velocity if the deflection on the air-water manometer is 1.0 mm? Air temperature = 10C, and p = I atm.

If the velocity in an airstream (p. = 98 kPa; T = l0C) is 24 m/s, what deflection will be produced in an air-water manometer if the stagnation tube is 2 mm in diameter?

What would be the error in velocity determination if one used a CP value of 1.00 for a circular stagnation tube instead of the true value? Assume the measurement is made with a stagnation tube 2 mm in diameter that is measuring air (T = 25C,p = 1 atm) velocity for which the stagnation pressure reading is 5.00 Pa.

A velocity-measuring probe used frequently for measuring smokestack gas velocities is shown. The probe consists of two tubes bent away from and toward the flow direction and cut off on a plane normal to tl1e flow direction, as shown. Assume the pressure coefficient is 1.0 at A and -0.4 at B. 1he probe is inserted in a stack where the temperature is 300C and the pressure is 100 k!'a absolute. The gas constant of the stack gases is 410 J/kg K. The probe is connected to a water manometer, and a 1.0 em dellection is measured. Calculate the stack gas velocity.

On the internet, locate technically sound resources relevant to the LOA. Skim these resources, and then a. Write down five findings that are relevant to engineering practice and interesting to you. b. Write down two questions about LDAs that are interesting and insightful.

Classify the following devices as to whether they are used to measure velocity (V), pressure (P), or discharge (Q). a. hot-wire anemometer b. venturi meter c. differential manometer d. orifice meter e. stagnation tube f. rotameter g. ultrasonic flow meter h. Bourdon-tube gage i. weir j. laser-Doppler anemometer

List five different instruments or approaches tllat engineer~ use to measure flow rate (discharge). For each instrument or approach, list two advantages and two disadvantages.

Water from a pipe is diverted into a tank for 3 min. If the weight of diverted water is measured to be 8 kN, what is the discharge in cubic meters per second? Assume the water temperature is 20C.

Water from a test apparatus is diverted into a calibrated volumetric tank for 6 min. If the volume of diverted water is measured to be 67 m', what is the discharge in cubic meters per second, gallons per minute, and cubic feet per second?

A velocity traverse in a 24-cm oil pipe yields the data in the table. What are the discharge, mean velocity, and ratio of maximum to mean velocity? Does the flow appear to be laminar or turbulent?

A velocity traverse inside a 16-in.-ci.rcular air duct yields the data in the table. What is the rate of flow in cubic feet per second and cubic feet per minute? What is the ratio of V mu to V m

The asymmetry of the flow in stacks means that flow velocity must be measured at several locations on the cross-flow plane. Consider the cross section of the cylindrical stack shown. The two access holes through which probes can be inserted arc separated by 90. Velocities can be measured at the five points shown (five-point method). a. Determine the ratio r ml D such that the areas of the five measuring segments are equal. b. Determine the ratio riD (probe location) that corresponds to the centroid of the segment. c. The data in the table are taken for a stack 2 m in diameter in which the gas temperature is 300C, the pressure is 110 kPa absolute, and the gas constant is 400 }/kg K. The data represent the deflection on a water manometer connected to a Pilot-static tube located at the measuring stations. Calculate the mass flow rate.

Repeat Prob. 13.17 for the case in which three access holes are separated by 60 and seven measuring points are used. "lhe diameter of the stack is 1.5 m, the gas temperature is 250C, the pressure is 115 kPa absolute, and the gas constant is 420 }/kg K. The data in the following table represent the deflection of a water manometer connected to a Pitot-static tube at the measuring stations. Calculate the mass flow rate.

lheory and experimental verification indicate that the mean velocity along a vertical line in a wide stream is closely approximated by the velocity at 0.6 depth. If the indicated velocities at 0.6 depth in a river cross section arc measured, what is the discharge in the river?

For the jet and orifice shown, determine Cv C,, and Cd.

A fluid jet discharging from a 4-cm orifice has a dian1eter of 3.7 em at its vena contracta. What is the coefficient of contraction?

Figure 13.14 on p. 488 of 13.2 is of a sharp-edged orifice. Note that the metal surface immediately downstream of the leading edge makes an acute angle with the metal of the upstream face of the orifice. Do you think the orifice would operate the same (have the same flow coefficient, K ) if that angle were 90? Explain how you carne to your conclusion.

New orifices such as that shown in Fig. 13.14 on p.488 of 13.2 will have definite flow coefficients as given in Fig. J 3.15 on p. 490 of~ 13.2. With age, however, physical changes could occur to the orifice. Explain what changes these might he and how (if at all) these physical changes might affect the flow coefficients.

A 6-in. orifice is placed in a I 0-in. pipe, and a mercury manometer is connected to either side of the orifice. If the flow rate of water (60F) through this orifice is 4.5 cfs, what will be the manometer deflection?

Determine the discharge of water through this 7-in. orifice that is installed in a 12-in. pipe. Assume T = 60F and v = 1.22 X 10-s ft2/s.

The flow coefficient values for orifices given in Fig. 13.15 on p. 490 of 13.2 were obtained by testing orifices in relatively smooth pipes. If an orifice were used in a pipe that was very rough, do you think you would get a valid indication of discharge by using the flow coefficient of Fig. 13.15? Justify your conclusion.

Determine the discharge of water (T = 60F) through the orifice shown if h = 4 ft, D = 6 in., and d = 3 in.

The 10-cm orifice in the horizontal30-cm pipe shown is the same size as the orifice in the vertical pipe. The manometers are mercury-water manometers, and water (T = 20C} is flowing in the system. The gages are Bourdon-tube gages. The flow, at a rate of 0.1 m3 /s, is to the right in the horizontal pipe and therefore downward in the vertical pipe. Is top as indicated by gages A and B the same as top as indicated by gages D and E? Determine their values. Is the deflection on manometer C the same as the deflection on manometer F? Determine the deflections.

If water (20C} is flowing through this 4.3-cm orifice, estimate the rate of flow. Assume flow coefficient K = 0.6.

A pressure transducer is connected across an orifice as shown. The pressure at the upstream pressure tap is p1, and the pressure at the downstream tap is p2 The pressure at the transducer connected to the upstream tap is Pr, 1 and to the downstream pressure tap,pr,2. Show that the difference in piezometric pressure defined as (p1 + -yz1) - (p1 + yz2) is equal to the pressure difference across the transducer,pT, 1 - Pr,2-

Water (T = 50F) is pumped at a rate of 20 cfs through the system shown in the figure. What differential pressure will occur across the orifice? What power must the pump supply to the flow for the given conditions? Also, draw the HGL and the EGL for the system. Assume f = O.DlS for the pipe.

Determine the size of orifice required in a 15-cm pipe to measure 0.03 m3 /s of water with a deflection of 1 mona mercury-water manometer.

What is the discharge of gasoline (S = 0.68) in a 12-cm horizontal pipe if the differential pressure across a 6-cm orifice in the pipe is 50 kPa?

What size orifice is required to produce a change in head of 6 m for a discharge of 2 m3 /s of water in a pipe 1 m in diameter?

An orifice is to be designed to have a change in pressure of 48 kPa across it (measured with a differential-pressure transducer) for a discharge of 4.0 m3 /s of water in a pipe 1.2 m in diameter. What diameter should the orifice have to yield the desired results?

Semicircular orifices such as the one shown are sometimes used to measure the flow rate of liquids that also transport sediments. The opening at the bottom of the pipe allows free passage of the sediment. Derive a formula for Q as a function of t:..p, D, and other relevant variables associated with the problem. Then, using that formula and guessing any unknown data, estimate the water discharge through such an orifice when up is read as 80 kPa and flow is in a 30-cm pipe.

What is the main advantage of a venturi meter versus an orifice meter? The main disadvantage?

What is the throat diameter required for a venturi meter in a 61 -cm horizontal pipe carrying water with a discharge of 0.76 m3 /s if the differential pressure between the throat and the upstream section is to be limited to 200 kPa at this discharge? For a first iteration, assume K = 1.02.

Estimate the rate of flow of water through the venturi meter shown

When no flow occurs through the venturi meter, the indicator on the differential-pressure gage is straight up and indicates a t:..p of zero. When 5 cfs of water flows to the right, the differential-pressure gage indicates tip = + 10 psi. If the flow is now reversed and 5 cfs flow to the left through the venturi meter, in which range would .1p fall? (a) j,p < - 10 psi, (b) -10 psi < tip < 0, (c) 0 < j,p < 10 psi, or( d) tip = 10 psi?

The pressure differential across this venturi meter is 92 kPa. What is the discharge of water (T = 20C) through it? [Hint: The value of flow coefficient you calculate should be K = 1.02)

Engineers are calibrating a poorly designed venturi meter for the flow of petroleum by relating the pressure difference between taps 1 and 2 to the discharge. By applying the Bernoulli equation and assuming a quasi-one-dimensional flow (velocity uniform across every cross section), the engineers find that On= Az[2(pl- Pz)lp] 05 [1- (d/D) 4 ] - 0 5 where D and dare the duct diameters at stations 1 and 2. However, they realize that the flow is not quasi-one-dimensional and that the pressure at tap 2 is not equal to the average pressure in the throat because of streamline curvature. Thus the engineers introduce a correction factor K into the foregoing equation to yield Q = KQo Use your knowledge of pressure variation across curved streamlines to decide whether K is larger or smaller than unity, and support your conclusion by presenting a rational argument.

The differential-pressure gage on the venturi meter shown reads 5.4 psi, h = 25 in., d = 7 in., and D = 12 in. What is the discharge of water in the system? Assume T = 50F.

The differential-pressure gage on the venturi meter reads 40 kPa, d = 20 em, D = 40 em, and h = 75 em. What is the discharge of gasoline (S = 0.69; 1.1.. = 3 X 10 4 N s/m2 ) in the system?

A flow nozzle has a throat diameter of 2 em and a beta ratio (d! D) of 0.5. Water flows through the nozzle, creating a pressure difference across the nozzle of 8 kPa. The viscosity of the water is I o-6 m2 /s, and the density is I 000 kg/m3 Find the discharge.

Water flows through an annular venturi consisting of a body of revolution mounted inside a pipe. The pressure is measured at the minimum area and upstream of the body. The pipe is 5 em in diameter, and the body of revolution is 2.5 em in diameter. A head difference of I m is measured across the pressure taps. Find the discharge in cubic meters per second.

A vortex flowmeter is used to measure the discharge in a duct 5 em in diameter. The diameter of the shedding element is I em. The Strouhal number based on the shedding frequency from one side of the element is 0.2. A signal frequency of 50 Hz is measured by a pressure transducer mounted downstream of the element. What is the discharge in the duct?

A rotameter operates by aerodynamic suspension of a weight in a tapered tube. The scale on the side of the rotameter is calibrated in scfm of air-that is, cubic feet per minute at standard conditions (p = 1 atm and T = 68F). By considering the balance of weight and aerodynamic force on the weight inside the tube, determine how the readings would be corrected for nonstandard conditions. ln other words, how would the actual cubic feet per minute be calculated from the reading on the scale, given the pressure, temperature, and gas constant of the gas entering the rotameter?

A rotameter is used to measure the flow rate of a gas with a density of 1.0 kglm3 .1he scale on the rotameter indicates 5 liters/s. However, the rotameter is calibrated for a gas with a density of 1.2 kg/m3 . What is the actual flow rate of the gas (in liters per second)?

Ultrasonic flowmeters are used to measure velocity in systems where it is important to not disrupt the flow, such as for blood velocity. One mode of operation of ultrasonic flowmeters is to measure the travel times between two stations for a sound wave traveling upstream and then downstream with the flow. The downstream propagation speed with respect to the measuring stations is c + V, where c is the sound speed and Vis the flow velocity. Correspondingly, the upstream propagation speed is c - V. a. Derive an expression for the flow velocity in terms of the distance between the two stations, L; the difference in travel times, 6.t; and the sound speed. b. The sound speed is typically much larger than V (c V). With this approximation, express V in terms of L, c, and 6.t. c. A 10-ms time difference is measured for waves traveling 20m in a gas where the speed of sound is 300 m/s. Calculate the flow velocity

On the Internet, locate technically reliable resources about weirs to answer the following questions. a. What are five important considerations for using weirs? b. What variables influence flow rate through a rectangularweir?

Water flows over a rectangular weir that is 2m wide and 30 em high. If the head on the weir is 10 em, what is the discharge in cubic meters per second?

The head on a 60 triangular weir is 25 em. What is the discharge over the weir in cubic meters per second?

Water flows over two rectangular weirs. Weir A is 5 ft long in a channellO ft wide; weir B is 5 ft long in a channelS ft wide. Both weirs are 2 ft high. If the head on both weirs is 1.00 ft, then one can conclude that (a)~ = QR, (b)~ > Qa, or (c)~ < Qa.

A 1-ft-high rectangular weir (weir I) is installed in a 2-ft-wide rectangular channel, and the head on the weir is observed for a discharge of 10 cfs. Then the 1-ft weir is replaced by a 2-ft-high rectangular weir (weir 2), and the head on the weir is observed for a discharge of 10 cfs. The ratio H 1/H2 should be (a) equal to 1.00, (b) less than 1.00, or (c) greater than 1.00.

Consider the rectangular weir described in Prob. 13.60. When the head is doubled, the discharge is (a) doubled, (b) less than doubled, or (c) more than doubled.

A basin is 50 ft long, 2 ft wide, and 4 ft deep. A sharp-crested rectangular weir is located at one end of the basin, and it spans the width of the basin (the weir is 2 ft long). The crest of the weir is 2 ft above the bottom of the basin. At a given instant water in the basin is 3 ft deep; thus water is flowing over the weir and out of the basin. Estimate the time it will take for the water in the basin to go from the 3 ft depth to a depth of 2 ft 2 in.

Water at 50F is piped from a reservoir to a channel like that shown. The pipe from the reservoir to the channel is a 4-in. steel pipe 100 ft in total length. There are two 90 bends, r/ D = I, in the line, and the entrance and exit are sharp edged. The weir is 2 ft long. The elevation of the water surface in the reservoir is 100 ft, and the elevation of the bottom of the channel is 70 ft. The crest of the weir is 3 ft above the bottom of the channel. For steady flow conditions determine the water surface elevation in the channel and the discharge in the system.

At one end of a rectangular tank I m wide is a sharpcrested rectangular weir I m high. In the bottom of the tank is a 10-cm sharp-edged orifice. If 0.10 m3 /s of water flows into the tank and leaves the tank both through the orifice and over the weir, what depth will the water in the tank attain?

What is the water discharge over a rectangular weir 3 ft high and 10ft long in a rectangular channel I 0 ft wide if the head on the weir is 1.5 ft?

A reservoir is supplied with water at 60F by a pipe with a venturi meter as shown. The water leaves the reservoir through a triangular weir with an included angle of 60. The flow coefficient of the venturi is unity, the area of the venturi throat is 12 in.2 , and the measured tlp is 10 psi. find the head, H, of the triangular weir

At a particular instant water flows into the tank shown through pipes A and B, and it flows out of the tank over the rectangular weir at C. The tank width and weir length (dimensions normal to page) are 2ft. Then, for the given conditions, is the water level in the tank rising or falling?

Water flows from the first reservoir to the second over a rectangular weir with a width-to-head ratio of 3. The height P of the weir is twice the head. The water from the second reservoir flows over a 60 triangular weir to a third reservoir. The discharge across both weirs is the same. Find the ratio of the head on the rectangular weir to the head on the triangular weir.

Given the initial conditions of Pro b. 13.68, tell, qualitatively and quantitatively, what will happen if the flow entering the first reservoir is increased 50%.

An engineer is designing a triangular weir for measuring the flow rate of a stream of water that has a discharge of 6 cfm. The weir has an included angle of 45 and a coefficient of discharge of 0.6. Find the head on the weir.

A pump is used to deliver water at l0C from a well to a tank. The bottom of the tank is 2m above the water surface in the weU. The pipe is commercial steel 2.5 m long with a diameter of 5 em. The pump develops a head of 20 m. A triangular weir with an included angle of 60 is located in a wall of the tank with the bottom of the weir 1 m above the tank floor. Find the level of the water in the tank above the floor of the tank.

A Pitol-static tube is used to measure the Mach number in a compressible subsonic flow of air. The stagnation pressure is 140 kPa, and the static pressure is I 00 kPa. The total temperature of the flow is 300 K. Determine the Mach number and the flow velocity.

Use the normal shock wave relationships developed in Chapter 12 to derive the Rayleigh supersonic Pilot formula.

The static and stagnation pressures measured by a Pi tot-static tube in a supersonic air flow are 54 kPa and 200 kPa, respectively. The total temperature is 350 K. Determine the Mach number and the velocity of the free stream.

A venturi meter is used to measure the flow of helium in a pipe. The pipe is 1 em in diameter, and the throat diameter is 0.5 em. The measured upstream and throat pressures are 120 kPa and 80 kPa, respectively. The static temperature of the helium in the pipe is l7C. Determine the mass flow rate.

Hydrogen at atmospheric pressure and l 5C flows through a sharp-edged orifice with a beta ratio, diD, of 0.5 in a 2-cm pipe. The pipe is horizontal, and the pressure change across the orifice is I kPa. The flow coefficient is 0.62.

A hole 0.2 in. in diameter is accidentally punctured in a line carrying natural gas (methane). The pressure in the pipe is 50 psig, and the atmospheric pressure is 14 psia. The temperature in the line is 70f. What is the rate at which the methane leaks through the hole (in lbm/s)? The hole can be treated as a truncated nozzle.

Consider the stagnation tube of Pro b. 13.5. Tf the uncertainty in the manometer measurement is 0.1 mm, calculate the velocity and the uncertainty in the velocity. Assume that CP = 1.00, p.,, = 1.25 kglm\ and the only uncertainty is due to the manometer measurement.

Consider the weir in Prob. 13.65. Calculate the discharge and the uncertainty in the discharge. Assume the uncertainty in K is 5%, in His 3 in., and in L is I in.