part a only Consider the simplified form of the continuity equation, Eq. 5.29 on p. 183

Consider filling the gasoline tank of an automobile at a gas station. (a) Estimate the discharge in gpm. (b) Using the same nozzle, estimate the time to put 50 gallons in the tank. (c) Estimate the cross-sectional area of the nozzle and calculate the velocity at the nozzle exit

The average flow rate (release) through Grand Coulee Dam is 110,000 ftl/s. The width of the river downstream of the dam is 100 yards. Making a reasonable estimate of the river velocity, estimate the river depth.

Taking a jar of known volume, fill with water from your household tap and measure the time to fill. Calculate the discharge from the tap. Estimate the cross-sectional area of the faucet outlet, and calculate the water velocity issuing from the tap.

Another name Or the volume flow rate equation could be: a. the discharge equation b. the mass flow rate equation c. either a or b

A liquid flows through a pipe with a constant velocity. If a pipe twice the size is used with the same velocity, will the flow rate be (a) halved, (b) doubled, (c) quadrupled? Explain.

For flow of a gas in a pipe, which form of the continuity equation is more general? a. V1A1 = V2A2 b. PtVIAt = P2V2A2 c. both are equally applicable

The discharge of water in a 35-cm-diameter pipe is 0.06 m3 /s. What is the mean velocity?

A pipe with a 18 in. diameter carries water having a velocity of 4 ft/s. What is the discharge in cubic feet per second and in gallons per minute (I cfs equals 449 gpm)?

A pipe with a 2 m diameter carries water having a velocity of 4 m/s. What is the discharge in cubic meters per second and in cubic feet per second?

Natural gas (methane) flows at 25 m/s through a pipe with a 0.84 m diameter. The temperature of the methane is I5C, and the pressure is 160 kPa gage. Determine the mass flow rate.

An aircraft engine test pipe is capable of providing a flow rate of 180 kgls at altitude conditions corresponding to an absolute pressure of 50 kPa and a temperature of -l8C.1he velocity of air through the duct attached to the engine is 255 m/s. Calculate the diameter of the duct.

A heating and air-conditioning engineer is designing a system to move 1000 m3 of air per hour at 100 kPa abs, and 30C. The duct is rectangular with cross-sectional dimensions of 1 m by 20 em. What will be the air velocity in the duct?

The hypothetical velocity distribution in a circular duct is V r - =1- - Vo R where r is the radial location in the duct, R is the duct radius, and V0 is the velocity on the axis. Find the ratio of the mean velocity to the velocity on the axis.

Water flows in a two-dimensional channel of width Wand depth D as shown in the diagram. The hypothetical velocity profLle for the water is V(x,y) = v,( 1 - )( 1 - ~:) here V, is the velocity at the water surface midway between the .:hannel walls. The coordinate system is as shown; xis measured from the center plane of the channel andy downward from the ;ater surface. Find the discharge in the channel in terms of V,, D, and W.

Water flows in a pipe that has a 4ft diameter and the llowing hypothetical velocity distribution: The velocity is "TJaximum at the centerline and decreases linearly with r to a :ninimum at the pipe wall. If Vmax = 15ft/sand Vmin = 12 ft/s, bat is the discharge in cubic feet per second and in gallons per minute?

In Prob. 5.16, if V max = 8 m/s, Vmiu = 6 m/s, and D = 2m, mat is the discharge in cubic meters per second and the mean d ocity?

Air enters thls square duct at section 1 with the ~locity distribution as shown. Note that the velocity varies in the direction only (for a given value of y, the velocity is the same l:lr all values of z). a. What is the volume rate of flow? b. What is the mean velocity in the duct? c. What is the mass rate of flow if the mass density of the air is 1.2 kg/m3 ?

The velocity at section A-A is 15 ft/s, and the vertical .;.epth y at the same section is 4ft. If the width of the channel is ' ft, what is the discharge in cubic feet per second?

If the velocity in the channel of Prob. 5.20 is given as u = 8[exp(y) - 1] m/s and the channel width is 2m, what is the discharge in the channel and what is the mean velocity?

Water from a pipe is diverted into a weigh tank for exactly 20 min. 'lhe increased weight in the tank is 20 kN. What is the discharge in cubic meters per second? Assume T = 20C.

Water enters the lock of a ship canal tluough 180 ports, each port having a 2 ft by 2 ft cross section. The lock is 900 ft long and 105ft wide. The lock is designed so that the water surface in it will rise at a maximum rate of 6ft/min. For this condition, what will be the mean velocity in each port?

An empirical equation for the velocity distribution in a horizontal, rectangular, open d1aJmel is given by u = u max (y!d)", where u is the velocity at a distance y feet above the floor of the channeL If the depth d of flow is 1.2 m, Umax = 3 rn/s, and n = 1/6, what is the discharge in cubic meters per second per meter of width of cha11nel? What is the mea11 velocity?

The hypothetical water velocity in a V-shaped channel (see the accompanying figure) varies linearly with depth from zero at the bottom to maximum at the water surface. Determine the discharge if the maximum velocity is 6 ft/s.

The velocity of flow in a circular pipe varies according to the equation VIV. = (I - rlra)", where V, is the centerline velocity, r0 is the pipe radius, and r is the radial distance from the centerline. The exponent n is general and is chosen to fit a given profile (n = I for laminar flow). Determine the mean velocity as a function of V. and n.

Plot the velocity distribution across the pipe, and determine the discharge of a fluid flowing through a pipe I m in diameter that has a velocity distribution given by V = 12( l - /r~) m!s. Here r0 is the radius of the pipe, and r is the radial distance from the centerline. What is the mean velocity?

Water flows through a 4.0-in.-diameter pipeline at 75 Ibm/min. Calculate the mean velocity. Assume T = 60F.

Water flows through a IS em pipeline at 700 kg/min. Calculate the mean velocity in meters per second if T = 20C.

A shell and tube heat exchanger consists of a one pipe inside another pipe as shown. The liquid flows in opposite directions in each pipe. If the speed of the liquid is the same in each pipe, what is the ratio of the outer pipe diameter to the inner pipe diameter if the discharge in each pipe is the same?

The cross section of a heat exchanger consists of three circular pipes inside a larger pipe. The internal diameter of the three smaller pipes is 2.5 em, and the pipe wall thickness is 3 mm. The inside diameter of the larger pipe is 8 cm.lf the velocity of the fluid in region between the smaller pipes and larger pipe is I 0 m/s, what is the discharge in m3 /s?

The mean velocity of water in a 6-in. pipe is 8.5 ft/s. Determine the flow in slugs per second, gallons per minute, and cubic feet per second if T = 60F.

Read 4.2, 5.2 and the internet to find answers to the following questions. a. What does the Lagrangian approach mean? What are three real-world examples that illustrate the Lagrangian approach? (Use examples that are not in the text.) b. What does the Eulerian approach mean? What are three real-world examples that illustrate the Eulerian approach? (Use examples that are not in the text.) c. What are three important differences between the Eulerian and the Lagrangian approaches? d. Why use an Eulerian approach? What are the benefits? e. What is a field? How is a field related to the Eulerian approach? f. What are the shortcomings of describing a flow field usiJ1g the Lagrangian description?

What is the difference between an intensive and extensive property? Give an example of each.

State whether each of the following quantities is extensive or intensive: a. mass b. volume c. density d. energy e. specific energy

What type of property do you get when you divide an extensive property by another extensive property-extensive or intensive? Hint: Consider density.

What is a control surface and a control volume? Can mass pass through a control surface?

In Fig 5.11 on p. 181 of ~5.2, a. the CV is passing through the system. b. the system is passing through the CV.

Gas flows into and out of the chamber as shown. Fur the conditions shown, which of the following statement(s) arc true of the application of the control volume equation to the continuity principle? a. Bsys = 0 b. dB,.,.)dt = 0 c. Lbp V A =d. ~ f p d J,l = 0 cv e. b = 0

The piston in the cylinder is moving up. Assume that the control volume is the volume inside the cylinder above the ~iston (the control volume changes in size as the piston moves) . . \ gaseous mixture exists in the control volume. For the given conditions, indicate which of the following statements are true. a. ~ p V A is equal to zero. b. -df p d 1s . equal to zero. dt cv c. 'Ihe mass density of the gas in the control volume is increasing with time. d. The temperature of the gas in the control volume is increasing with time. e. The flow inside the control volwne is unsteady.

For cases a and b shown in the figure, respond n the following questions and statements concerning the 1pplication of the Reynolds transport theorem to the tinuity equation. a. What is the value of b? b. Determine the value of dB,y,ldt. c. Determine the value of ~ bp V A. cs d. Determine the value of dldt f bpd.

The law of conservation of mass for a closed system requires that the mass of the system is a. constant b. zero

part a only Consider the simplified form of the continuity equation, Eq. 5.29 on p. 183 of 5.3. An engineer is using this equation to find the Qc of a creek at the confluence with a large river because she has automatic electronic measurements of the river discharge upstream, ORu and downstream, QRd of the creek confluence. a. Which of the three terms on the left-hand side of Eq. 5.29 will the engineer assume is zero? Why? b. Sketch the creek and the river and sketch the CV you would select to solve this problem.

A pipe flows full with water. Is it possible for the volume flow rate into the pipe to be different than the flow rate out of the pipe? Explain

Air is pumped into one end of a tube at a certain mass flow rate. Is it necessary that the san1e mass flow rate of air comes out the other end of the tube? Explain.

If an automobile tire develops a leak, how does the mass of air and density change inside the tire with time? Assuming the temperature remains constant, how is the change in density related to the tire pressure?

Two pipes are connected together in series. The diameter of one pipe is twice the diameter of the second pipe. With liquid flowing in the pipes, the velocity in the large pipe is 4 m/s. What is the velocity in the smaller pipe?

Two parallel disks of diameter Dare brought together, each with a normal speed of V. When their spacing ish, what is the radial component of convective acceleration at the section just inside the edge of the disk (section A) in terms of V, h, and D? Assume uniform velocity distribution across the section.

Two streams discharge into a pipe as shown. The flows are incompressible. The volume flow rate of stream A into the pipe is given by ~ = 0.04t ml/s and that of strean1 B by Q8 = 0.006 t? m3 /s, where tis in seconds. The exit area of the pipe is 0.01 m2 Find the velocity and acceleration of the flow at the exit at t = 1 s.

Air discharges downward in the pipe and then outward between the parallel disks. Assuming negligible density change in the air, derive a formula for the acceleration of air at point A, which is a distance r from the center of the disks. Express the acceleration in terms of the constant air discharge Q, the radial distance r, and the disk spacing h. If D = 10 em, h = 0.6 em, and Q = 0.380 m3 /s, what are the velocity in the pipe and the acceleration at point A where r = 20 em?

AlI the conditions of Prob. 5.53 ar e the san1e except that h = 1 em and the discharge is given as Q = Q0 (t/t 0), where Q0 == O.l m3 /s and 10 == Is. For the additional conditions, what will be the acceleration at point A when t == 2 s and t == 3 s?

A tank has a hole in the bottom with a crosssectional area of 0.0025 m2 and an inlet line on the side with a cross-sectional area of 0.0025 m2 , as shown. The cross-sectional area of the tank is 0.1 m2 The velocity of the liquid flowing out the bottom hole is V = v'2gfi, where h is the height of the water surface in the tank above the outlet. At a certain time the surface level in the tank is 1 m and rising at the rate of 0.1 cm/s. The liquid is incompressible. Find the velocity of the liquid through the inlet.

A mechanical pump is used to pressurize a bicycle tire. The inflow to the pwnp is 0.8 cfm. The density of the air entering the pump is 0.075 lbmtfe. The inflated volume of a bicycle tire is 0.035 frl. The density of air in the inflated tire is 0.4 lbmtfe. How many seconds does it take to pressurize the tire if there initially was no air in the tire?

A 6-in.-diameter cylinder falls at a rate of 4 ft/s in an 8-in.-diameter tube containing an incompressible liquid. What is the mean velocity of the liquid (with respect to the tube) in lhe space between the cylinder and the tube wall?

This circular tank of water is being filled from a pipe as shown. The velocity of flow of water from the pipe is 10 ft/s. What will be the rate of rise of the water surface in the tank?

A sphere 8 inches in diameter falls at 4 ft/s downward axially through water in a 1-ft-diameter container. Find the upward speed of the water with respect to the container wall at the midsection of the sphere.

A 30 em pipe divides into a 20 em branch and a 18 em branch. If the total discharge is 0.40 m3 /s and if the same mean velocity occurs in each branch, what is the discharge in each branch?

The conditions are the same as in Prob. 5.61 except that the discharge in the 20 em branch is twice that in the 15 em branch. Vhat is the mean velocity in each branch?

Water flows in a 10 in. pipe that is connected in series with a 6 in. pipe. If the rate of flow is 898 gpm (gallons per minute), what is the mean velocity in each pipe?

What is the velocity of the flow of water in leg B of the tee .hown in the figure?

For a steady flow of gas in the conduit shown, what is :he mean velocity at section 2?

Two pipes, A and B, are connected to an open water tank. :he Water is entering the bottom of the tank from pipe A at 10 cfm. ""be water level in the tank is rising at 1.0 in./ min, and the surface area of the tank is 80 If. Calculate the discharge in a second pipe, p~pe B, that is also connected to the bottom of the tank. Is the low entering or leaving the tank from pipe B?

Is the tank in the figure filling or emptying? At what rate is the water level rising or falling in the tank?

Given : Flow velocities as shown in the figure and water surface elevation (as shown) all = 0 s. At the end of 22 s, will the water surface in the tank be rising or falling, and at what speed?

A lake with no outlet is fed by a river with a constant flow of 1200 frl/s. Water evaporates from the surface at a constant rate of 13 ft 3 /s per square mile surface area. The area varies with depth h (feet) as A (square miles) = 4.5 + 5.5h. What is the equilibrium depth of the lake? Below what river discharge will the lake dry up?

An open tank has a constant inflow of 20 ft3 /s. A LO-ftdiameter drain provides a variable outflow velocity V""' equal to V[2iJi'j ft/s. What is the equilibrium height h.q of the liquid in the tank?

Assuming that complete mixing occurs between the two inflows before the mixture discharges from the pipe at C, find the mass rate of flow, the velocity, and the specific gravity of the mixture in the pipe at C.

Oxygen and methane are mixed at 200 kPa absolute pressure and l00C. lhe velocity of the gases into the mixer is 5 m/s. The density of the gas leaving the mixer is 1.9 kg/rn3 Determine the exit velocity of the gas mixture.

A pipe with a series of holes as shown in the figure is used in many engineering systems to distribute gas into a system. The volume flow rate through each hole depends on the pressure difference across the hole and is given by ( 2t:.p)ll2 Q = 0.67 A0 -pwhere A0 is the area of the hole, t:.p is the pressure difference across the hole, and p is the density of the gas in the pipe. If the pipe is sufficiently large. the pressure will be uniform along the pipe. A distribution pipe for air at 20 C is 0.5 meters in diameter and 10m long. The gage pressure in the pipe is 100 Pa. The pressure outside the pipe is atmospheric at I bar. The hole diameter is 2.5 ern, and there are 50 holes per meter length of pipe. The pressure is constant in the pipe. Find the velocity of the air entering the pipe.

The globe valve shown in the figure is a very common device to control flow rate. The flow comes through the pipe at the left and then passes through a minimum area formed by the disc and valve seat. As the valve is dosed, the area for flow between the disc and valve is reduced. The flow area can be approximated by the annular region between the disc and the seat. The pressure drop across the valve can be estimated by application of the Bernoulli equation between the upstream pipe and the opening between the disc and valve seat. Assume there is a I 0 gpm (gallons per minute) flow of water at 60F througn the valve. The inside diameter of the upstream pipe is 1 inch. The distance across the opening from the disc to the seat is 1/Sth of an incn, and the diameter of the opening is 1/2 inch. What is the pressure drop across the valve in psid?

In the flow through an orifice shown in the diagram the flow goes through a minimum area downstream of the orifice. This is called the "vena contracta: The ratio of the flow area at the vena contracta to the area of the orifice is 0.64. a. Derive an equation for the discharge through the orifice in the form Q = CA"(2t:.p/p)tll, where A0 is the area of the orifice, t:.p is the pressure difference between the upstream flow and the vena contracta, and p is the fluid density. Cis a dimensionless coefficient. b. Evaluate the discharge for water at 1000 kg/m1 and a pressure difference of 10 kPa for a 1.5 em orifice centered in a 2.5-cm diameter pipe.

A compressor supplies gas to a I 0 m tank. The in et mass flow rate is given by rn = 0.5 p0 /p {kg/s), where pis the density in the tank and p0 is the initial density. Find the time it would take to increase the density in the tank by a factor of 2 if the initial density is 2 kg!m3 Assume the density is uniform throughout the tank.

A slow leak develops in a tire (assume constant volume), in ,1Jich it takes 3 hr for the pressure to decrease from 30 psig to :5 psi g. The air volume in the tire is 0.5 ft \and the temperature t>mains constant at 60F. The mass flow rate of air is given by '"' = 0.68 pAIVRT. Calculate tht! area of the hole in the tire. '.tmospheric pressure is 14 psia.

Oxygen leaks slowly through a small orifice in an "l)'gCD bottle. The volume of the bottJe is 0.1 m3 , and the :.;ameter of the orifice is 0.12 mm. The temperature in the tank cmains constant at l8C, and the mass flow rate is given by = 0.68 pA I V RT. How long will it take the absolute pressure decrease from 10 to 5 MPa?

A cylindrical drum of water, lying on its side, is being -::1ptied through a 2 ir1.- diameter short pipe at the bottom of the ~.The velocity of the water out of the pipe is V = v'2gh, 'lere g is the acceleration due to gravity and fr is the height of the water surface above the outlet of the tank. The tank is 4 ft long and 2ft in diameter. Initially the tank is half full. Find the time for the tank to empty.

Water is draining from a pressurized tank as shown in the figure. The exit velocity is given by ,= ~gh where pis the pressure in the tank, p is the water density, and h is the elevation of the water surface above the outlet. The depth of the water in the tank is 2m. The tank has a erosssectional area of 1 m2 , and the exit area of the pipe is I 0 cm2 The pressure in the tank is maintained at 10 kPa. Find the time required to empty the tank. Compare this value with the time required if the tank is not pressurized.

For the type of tank shown, tl1e tank diameter is given as D = d + C1 h, where d is the bottom diameter and C1 is a constant. Derive a formula for the lime of fall of liquid surface from II = fr0 to h = h in terms of di, d, h0, h, and C1. Solve fort if h0 = 1 m, h = 20 em, d = 20 em, C1 = 0.3, and d1 = 5 em. The velocity of water in the liquid jet exiting tl1e tank is V, = v'2jh.

A spherical tank with a diameter of I rn is half filled with water. A port at the bottom of the tank is opened to drain the tank. The hole diameter is t em, and the velocity of the water draining from the hole is V, = v'2ifi, where his the elevation of the water surface above the hole. Find the time required for the tank to empty.

A tank containing oil is to be pressurized to decrease the draining time. The tank, shown in the figure, is 2m in diameter and 6 m high. The oil is originally at a level of 5 m. The oil has a density of 880 kg/m3 The outlet port has a diameter of 2 em, and the velocity at the outlet is given by v, = J2gh + 2 : where p is the gage pressure in the tank, p is the density of the oil, and his the elevation of the surface above the hole. Assume during the emptying operation that the temperature of the air in the tank is constant.1l1e pressure will vary as (L - h0) P = (Po + Patm) (L _ h) - Patm where Lis the height of the tank, Patm is the atmospheric pressure, and the subscript 0 refers to the initiaJ conditions. The initial pressure in the tank is 300 kPa gage, and the atmospheric pressure is 100 kPa.Applying the continuity equation to this problem, one finds dh = _ Ae J 2gh + 2p dt Ar p Integrate this equation to predict the depth of the oil with time for a period of one hour.

Rocket Propulsion. To prepare for problems 5.87, 5.88, and 5.89, use the Internet or other resources and define the following terms in the context of rocket propulsion: (a) solid fuel, (b) grain, and (c) surface regression. Also explain how a solid-fuel rocket engine works.

An end-burning rocket motor has a chamber diameter of l 0 em and a nozzle exit diameter of 8 em. The density of the solid propellant is 1800 kg/m3 , and the propellant surface regresses at the rate of 1.5 cm/s. The gases crossing the nozzle exit plane have a pressure of I 0 k.Pa abs and a temperature of 2200C. The gas constant of the exhaust gases is 415 )/kg K. Calculate the gas velocity at the nozzle exit plane.

A cylindrical-port rocket motor has a grain design consisting of a cylindrical shape as shown. The curved internal surface and both ends bum. The solid propellant surface regresses uniformly all cm/s. The propellant density is 2000 kg/m3 The inside diameter of the motor is 20 em. The propellant grain is 40 em long and has an inside diameter of 12 em. The diameter of the nozzle exit plane is 20 em. The gas velocity at the exit plane is 1800 m/s. Determine the gas density at tl1e exit plane.

The mass flow rate through a rocket nozzle (shown) is given by . p,A, m = 0.65 , rn;r; vRT, where p, and "fc are the pressure and temperature in the rocket chamber and R is the gas constant of tl1e gases in the chamber. 1he propellant burning rate (surface regression rate) can be expressed as r = ap~. where a and n are two empirical constants. Show, by application of the continuity equation, that the chamber pressure can be expressed as = ( app )1/(1-n)(AR)l/(1 n) (RT,)"I:l(t-n)l p, 0.65 A,.,.here Pp is the propellant density and Ag is the grain surface ;:,urning area. If the operating chamber pressure of a rocket motor is 3.5 MPa and n = 0.3, how much will the chamber "ressure increase if a crack develops in the grain, increasing me burning area by 20%?

Gas is flowing from Location 1 to 2 in the pipe apansion shown. The inlet density, diameter and velocity are p1, .;:),, and V1 respectively. If D2 is 2D1 and V2 is half of V1, what is :!le magnitude of p2? a. P2 = 4 P1 b. P2 = 2 PI c. P2 = '/2 PI d. Pz = P1

Air is flowing from a ventilation duct (cross section I) as 'lawn, and is expanding to be released into a room at cross section 2.The area at cross section 2,A2,is 3 times A1 Assume that the density is constant. The relation between Q1 and Q2 is: a. 02 = '/; 01 b. Q2 = Ql c. Qz = 3 01 d. Qz = 9 01

Water is flowing from Location I to 2 in this pipe expansion. D1 and V1 are known at the inlet. D2 and P2 are known at the outlet. What equation(s) do you need to solve for the inlet pressure P1? Neglect viscous effects. a. The continuity equation b. The continuity equation and the flow rate equation c. The continuity equation, the flow rate equation, and the Bernoulli equation d. There is insufficient information to solve the problem

The flow pattern through the pipe contraction is as shown, and the Q of water is 60 cfs. For d = 2 ft and D = 6 ft, what is the pressure at point B if the pressure at point Cis 3200 psf?

Water flows through a rigid contraction section of circular pipe in which the outlet diameter is one-half tl1e inlet diameter. The velocity of the water at the inlet varies with time as V10 = (10 m/s) [1 - exp(- t/10)]. How will the velocity vary with time at the outlet?

The annular venturi meter is useful for metering flows in pipe systems for which upstream calming distances are limited. The annular venturimetcr consists of a cylindrical section mounted inside a pipe as shown. The pressure difference is measured between the upstream pipe and at the region adjacent to the cylindrical section. Air at standard conditions flows in the system. The pipe diameter is 6 in. The ratio of the cylindrical section diameter to the inside pipe diameter is 0.8. A pressure difference of 2 in of water is measured. Find the volume flow rate. Assume the flow is incompressible, in viscid, and steady and that the velocity is uniformly distributed across the pipe.

Venturi-type applicators are frequently used to spray liquid fertilizers. Water flowing through the venturi creates a subatmospheric pressure at the throat, which in turn causes the liquid fertilizer to Oow up the feed tube and mix with the water in the throat region. The venturi applicator shown uses water at 20C to spray a liquid fertilizer with the same density. The venturi exhausts to the atmosphere, and the exit diameter is I em. The ratio of exit area to throat area (A)A 1) is 2. The flow rate of water through the venturi is 8 1./m (liters/min). The bottom of the feed tube in the reservoir is 5 em below the liquid fertilizer surface and I 0 em below the centerline of the venturi. The pressure at the liquid fertilizer surface is atmospheric. The flow rate through the feed tube between the reservoir and venturi throat is Q,(L!min) = o.sv'irli where tlh is the drop in piezometric head (in meters) between the feed tube entrance and the venturi centerline. Find the flow rate of liquid fertilizer in the feed tube, Q1 Also find the concentration of liquid fertilizer in the mixture, [Q1/(Q1 + Qwll. at the end of the sprayer.

Air with a density of 0.0644lbm/ft3 is flowing upward in the vertical duct, as shown. The velocity at the inlet (station 1) is 80 ft/s, and the area ratio between stations I and 2 is 0.5 (A2/ A1 = 0.5). Two pressure taps, 10 ft apart, are connected to a manometer, as shown. The specific weight of the manometer liquid is 120 lbf/ft3 Find the deflection, tlh, of the manometer.

An atomizer utilizes a constriction in an air duct as shown. Design an operable atomizer making your own assumptions regarding the air source.

A design for a hovercraft is shown in the figure. A fan brings air at 60F into a chamber, and the air is exhausted between lhe skirts and the ground. The pressure inside the chamber is responsible for the lift. The hovercraft is 15 ft long and 7ft wide. The weight of the craft including crew, fuel, and load is 2000 lbf. Assume that the pressure in the chamber is the stagnation pressure (zero velocity) and the pressure where the air exits around the skirt is atmospheric. Assume the air is incompressible, the flow is steady, and viscous effects are negligible. Find the airflow rate necessary to maintain the skirts at a height of 3 inches above the ground.

Water is forced out of this cylinder by the piston. Tf the .. ton is driven at a speed of 6 ft/s, what will be the speed of ilux of the water from the nozzle if d = 2 in. and D = 4 in.? ecting friction and assuming irrotational flow, determine the rce F that will be required to drive the piston. The exit pressure atmospheric pressure.

Air flows through a constant-area heated pipe. At the -trance, the velocity is 10 m/s, the pressure is 100 kPa absolute, -d the temperature is 20C. At the outlet, the pressure is 80 kPa .;{))Ute, and the temperature is 50C. What is the velocity at the ..det? Can the Bernoulli equation be used to relate the pressure J velocity changes? Explain.

Sometimes driving your car on a hot day, you may - ounter a problem with the fuel pump called pump cavitation. 'lal is happening to the gasoline? How does this affect the ""<:ration of the pump?

What is cavitation? Why does the tendency for cavitation .A liquid increase with increased temperatures?

The following questions have to do with cavitation. a. Is it more correct to say that cavitation has to do with (i) vacuum pressures, or (ii) vapor pressures? b. Ts cavitation more likely to occur on the low pressure (suction) side of a pump, or the high pressure (discharge) side? Why? c. What does the word cavitation have to do with cavities, like the ones we get in our teeth? Is this aspect of cavitation the (i) cause, or the (ii) result of the phenomenon? d. When water goes over a waterfall, and one can see lots of bubbles in the water, is that due to cavitation? Why, or why not?

When gage A indicates a pressure of 130 k.Pa gage, then . tation just starts to occur in the venturi meter. If D = 50 em and d = 10 em, what is the water discharge in the system for this condition of incipient cavitation? The atmospheric pressure is 100 kPa gage, and the water temperature is l0C. Neglect gravitational effects.

A sphere L ft in diameter is moving horizontally at a depth of I 2 ft below a water surface where the water temperature is 50F. v max = 1.5 v . where v. is the free stream velocity and occurs at the maximum sphere width. At what speed in still water will cavitation first occur?

When the hydrofoil shown was tested, the minimum pressure on the surface of the foil was found to be 70 kPa absolute when the foil was submerged 1.80 m and towed at a speed of 8 m/s. At the same depth, at what speed will cavitation first occur? Asswne irrotational flow for both cases and T = l0C.

When the hydrofoil shown was tested, the minimum pressure on the surface of the foil was found to be 2.5 psi vacuum when the foil was submerged 4 ft and towed at a speed of 25 ft/s. At the same depth, at what speed will cavitation first occur? Assume irrotational flow for both cases and T = 50F.

For the conditions ofProb. 5.11 L, at what speed will cavitation begin if the depth is increased to 10 ft?

A sphere is moving in water at a depth where the absolute pressure is 18 psia. The maxirmun velocity on a sphere occurs 90 from the forward stagnation point and is 1.5 times the freestream velocity. The density of water is 62.4lbm/ft3 Calculate the speed of the sphere at which cavitation will occur. T = 50F.

The minimum pressure on a cylinder moving horizontally in water (T = I0C) at 5 m/s at a depth of 1m is 80 kPa absolute . At what velocity will cavitation begin? Atmospheric pressure is I 00 kPa absolute .