The velocity along a pathline is given by V (mls) = s 2 t 112 where sis in meters and

If somehow you could attach a light to a fluid particle and :ake a time exposure photo, would the image you photographed "e a pathline or streakline? Explain from definition of each.

Is the pattern produced by smoke rising from a chimney on a windy day analogous to a path line or streakline? Explain from :he definition of each.

A windsock is a sock-shaped device attached to a swivel 10 top of a pole. Wmdsocks at airports are used by pilots to see mstantaneous shifts in the direction of the wind. If one drew a line co-linear with a windsock's orientation at any instant, the line would be best approximate a (a) pathline, (b) streakli.ne, or (c) streamline.

For streamlines, streaklines, and streamlines to all be co-linear, the flow must be a. dividing b. stagnant c. steady d. a tracer

At time t = 0, dye was injected at point A in a flow field of a .1quid. When the dye had been injected for 4 s, a path line for a particle of dye that was emitted at the 4 s instant was started. The streakline at the end of 10 s is shown below. Assume that the speed 'but not the velocity) of flow is the same throughout the 10 s period. Draw the pathli.ne of the particle that was emitted at t = 4 s. Make "Our own assumptions for any missing information.

For a given hypothetical flow, the velocity from time t = 0 to = 5 s was u = 2 m/s, v = 0. Then, from time I = 5 s to I = 10 s, ihe velocity was u = + 3 m/s, v = - 4 m/s. A dye streak was narted at a point in the flow field at time t = 0, and the path of a particle in the fluid was also traced from that same point starting at the same time. Draw to scale the streakline, path line of the ?article, and streamlines at timet= 10 s.

At time t = 0, a dye streak was started at point A in a flow field of liquid. The speed of the flow is constant over a 10 s period, but the flow direction is not necessarily constant. At any particular instant the velocity in the entire field of flow is the ~e. The streakline produced by the dye is shown above. Draw and label) a streamline for the flow field at t = 8 s. Draw (and label) a pathline that one would see at t = 10 s for a particle of dye that was emitted from point A at t = 2 s.

A velocity field is given mathematically as V = 2i + 4yj. The velocity field is: a. !Dinx b. lD in y c. 20 in x and y

There is a gasoline spill in a major river. The mayor of a large downstream city demands an estimate of how many hours it will take for the spill to get to the water supply plant intake. l11e emergency responders measure the speed of the leading edge of the spill, effectively focusing on one particle of fluid. Meanwhile, environmental engineers at the local university employ a computer model, which simulates the velocity field for any stage of the river, and for all locations (including steep narrow canyon sections with fast velocities, and an extremely wide reach with slow velocities). To compare these two mathematical approac~es, which statement is most correct? a. The responders have an Eulerian approach, and the engineers have a Lagrangian one b. The responders have a Lagrangian approach, and the engineers have an Eulerian one.

You are pouring a heavy syrup on your pancakes. As the syrup spreads over the pancake, would the thin film of syrup be a laminar or turbulent flow? Why?

A velocity field is given by V = 1 Oxyi . It is a. 1-D and steady b. 1-D and unsteady c. 2-0 and steady d. 2-D and unsteady

Which is the most correct way to characterize turbulent flow? a. 10 b. 20 c. 30

In the system in the figure, the valve at Cis gradually opened in such a way that a constant rate of increase in discharge is produced. How would you classify the flow at B while the valve is being opened? How would you classify the flow at A?

Water flows in the passage shown. If the flow rate is decreasing with time, the flow is classified as (a) steady, (b) unsteady, (c) uniform, or (d) nonuniform.

If a flow pattern has converging streamlines, how would you classify the flow?

Consider flow in a straight conduit. The conduit is circular in cross section. Part of the conduit has a constant diameter, and part has a diameter that changes with distance. Then, relative to flow in that conduit, correctly match the items in column A with those in column B. A B Steady flow av,tas = o Unsteady flow av,tas 0 Uniform flow iiV,Iat = 0 Nonuniform flow iJV,IiJt >"

Classify each of the following as a one-dimensional, twodimensional, or three-dimensional flow. a. Water flow over the crest of a long spillway of a dam. b. Flow in a straight horizontal pipe. c. Flow in a constant-diameter pipeline that follows the contour of the ground in hilly country. d. Airflow from a slit in a plate at the end of a large rectangular duct. e. Airflow past an automobile. f. Airflow past a house. g. Water flow past a pipe that is laid normal to the flow across the bottom of a wide rectangular channel.

Acceleration is the rate of change of velocity with time. Js the acceleration vector always aligned with the velocity vector? Explain.

In a flowing fluid, acceleration means that a fluid particle is a. changing direction b. changing speed c. changing both speed and direction d. any of the above

The flow passing through a nozzle is steady. The speed of the fluid increases between the entrance and the exit of the nozzle. The acceleration halfway between the entrance and the nozzle is a. convective b. local c. both

Local acceleration a. is dose to the origin b. is quasi nonuniform c. occurs in unsteady flow

Figure 4.36 on p. 148 in 4.10 shows the flow pattern for flow past a circular cylinder. Assume that the approach velocity at A is constant (does not vary with time). a. Is the flow past the cylinder steady or unsteady? b. Is this a case of one-dimensional, two-dimensional, or three-dimensional flow? c. Are there any regions of the flow where local acceleration is present? If so, show where they are and show vectors representing the local acceleration in the regions where it occurs. d. Are there any regions of flow where convective acceleration is present? If so, show vectors representing the convective acceleration in the regions where it occurs.

The velocity along a pathline is given by V (mls) = s 2 t 112 where sis in meters and tis in seconds. The radius of curvature is 0.4 m. Evaluate the acceleration tangent and normal to the path at s = 1.5 m and t = 0.5 seconds.

Tests on a sphere are conducted in a wind tunnel at an air speed of U0 The velocity of flow toward the sphere along the longitudinal axis is found to be u = - U0 (I - ~/_xl), where r0 is the radius of the sphere and x the distance from its center. Determine the acceleration of an air particle on the x-axis upstream of the sphere in terms of x, r0 , and U0

In this flow passage the velocity is varying with time. The elocity varies with time at section A-A as t V = 5 m/s - 2.25 - m/s /o : time t = 0.50 s, it is known that at section A-A the velocity ;;radient in the s direction is +2 m/s per meter. Given that t0 is 5 sand assuming quasi-one-dimensional flow, answer the Uowing questions for time t = 0.5 s. a. What is the local acceleration at A-A? b. What is the convective acceleration at A-A?

The nozzle in the figure is shaped such that the d ocity of flow varies linearly from the base of the nozzle to u tip. Assuming quasi-one-dimensional flow, what is the nvective acceleration midway between the base and the tip if e velocity is 1 ft/s at the base and 4 ft/s at the lip? Nozzle length 18 inches.

In Prob. 4.28 the velocity varies linea.rly with time .roughout the nozzle. The velocity at the base is 21 (fl/s) and at e tip is 6t (ftls). What is the local acceleration midway along "'e nozzle when t = 2 s?

What will be the convective acceleration for the conditions of Prob. 4.30?

The velocity of water flow in the nozzle shown is given by the following expression: V = 2t/(1 - O.Sx/ L)2 , where V = velocity in feet per second, t = time in seconds, x = distance along the nozzle, and L = length of nozzle = 4 ft. When x = 0.5L and t = 3 s, what is the local acceleration along the centerline? What is the convective acceleration? Assume quasi-one-dimensional flow prevails.

State Newton's second law of motion. What arc the limitations on the use of Newton's second law? Explain.

What is the differences between a force due to weight and a force due to pressure? Explain.

A pipe slopes upward in the direction ofliquid flow at an angle of 30 with the horizontal. What is the pressure gradient in the flow direction along the pipe in terms of the specific weight of the liquid if the liquid is decelerating (accelerating opposite to flow direction) at a rate of 0.4 g?

What pressure gradient is required to accelerate kerosene (S = 0.81) vertically upward in a vertical pipe at a rate ofO.S g?

The hypothetical liquid in the tube shown in the figure has zero viscosity and a specific weight of 10 kN/m3 If PR- PAis equal to 12 kPa, one can conclude that the liquid in the tube is being accelerated (a) upward, (b) downward, or (c) neither: acceleration = 0.

If the piston and water (p = 62.4lbm/ft3 ) are accelerated upward at a rate of 0.4g, what will be the pressure at a depth of 2ft in the water column?

Water (p = 62.4 lbm/ftl) stands at a depth of 10ft in a vertical pipe that is open at the top and closed at the bottom by a piston. What upward acceleration of the piston is necessary to create a pressure of 8 psig immediately above the piston?

Water (p = 1000 kg/m3 ) is accelerated from rest in a horizontal pipe that is 80 m long and 30 em in diameter. If the acceleration rate (toward the downstream end) is 5 m/s 2 , what is the pressure at the upstream end if the pressure at the downstream end is 90 kPa gage?

Water (p = 62.4lbm/ft3 ) stands at a depth of 10ft in a vertical pipe that is closed at the bottom by a piston. Assuming that the vapor pressure is zero (abs), determine the maximum downward acceleration that can be given to the piston without causing the water immediately above it to vaporize.

A liquid with a specific weight of 100 lbf/ftl is in the conduit. This is a special kind of liquid that has zero viscosity. The pressures at points A and Bare 170 psf and 100 psf, respectively. Which one (or more) of the following conclusions can one draw with certainty? (a) The velocity is in the positive e direction. (b) The velocity is in the negative e direction. (c) The acceleration is in the positive f direction. (d) The acceleration is in the negative e direction.

If the velocity varies linearly with distance through this water nozzle, what is the pressure gradient, dp/dx, halfway through the nozzle? (p = 62.4 lbm/ft 3 ) .

The closed tank shown, which is full of liquid, is accelerated downward at 1.5g and to the right at 0.9g. Here L = 3ft, H = 4ft, and the specific gravity of the Liquid is 1.2. Determine Pc - PA andpR- PA

The closed tank shown, which is full of liquid, is accelerated downward at ig- and to the right at lg. Here L = 2.5 m, H = 3 m, and the liquid has a specific gravity of 1.3. Determine Pc - PA and PB - PA

Describe in your own words how an aspirator works

When the Bernoulli Equation applies to a venturi, such as in Fig. 4.27 on p. 134 in 4.6, which of the following are true? (Select all that apply.) a. If the velocity head and elevation head increase, then the pressure head must decrease. b. Pressure always decreases in the direction of flow along a streamline. c. The total head of the flowing fluid is constant along a streamline

A water jet issues vertically from a nozzle, as shown. The water velocity as it exits the nozzle is 18 m/s. Calculate how high h the jet will rise. (Hint: Apply the Bernoulli equation along the centerline.)

ater flows through a vertical contraction (venturi) ..ection. Piezometers are attached to the upstream pipe and ::nmimum area section as shown. The velocity in the pipe is 10 ft/s. ne difference in elevation between the two water levels in the "'tezometers is 6 inches. The water temperature is 68F. What is he velocity (ft/s) at the minimum area?

Kerosene at 20C flows through a contraction section . shown. A pressure gage connected between the upstream pipe -,d throat section shows a pressure difference of 20 kPa. The line velocity in the throat section is 8 m/s. What is the 'docity (m/s) in the upstream pipe?

A stagnation tube placed in a river (select all that apply) a. can be used to determine air pressure b. can be used to determine fluid velocity c. measures kinetic pressure

A Pitot-static tube is mounted on an airplane to measure airspeed. At an altitude of 10,000 ft, where the temperature is 23F and the pressure is 10 psia, a pressure difference corresponding to 10 in of water is measured. What is the airspeed?

A glass tube is inserted into a flowing stream of water with one opening directed upstream and the other end vertical. If the water velocity is 5 m/s, how high will the water rise in the vertical leg relative to the level of the water surface of the stream?

A Bourdon-tube gage is taped into the center of a disk as shown. Then for a disk that is about 1 ft in diameter and for an approach velocity of air ( V0 ) of 40 ft/s, the gage would read a pressure intensity that is (a) less than p V~/2, (b) equal top V512, or (c) greater than p V5!2.

An air-water manometer is connected to a Pilot-static tube used to measure air velocity. If the manometer deflects 2 in., what is the velocity? Assume T = 60F and p = 15 psia.

The flow-metering device shown consists of a stagnation probe at station 2 and a static pressure tap at station 1. The velocity at station 2 is 1.5 times that at station LAir with a density of 1.2 kglm3 flows through the duct. A water manometer is connected between the stagnation probe and the pressure tap, and a deflection of 10 em is measured. What is the velocity at station 2?

The "spherical" Pitot probe shown is used to measure the flow velocity in water (p = 1000 kg/m1 ). Pressure taps are located at the forward stagnation point and at 90 from the forward stagnation point. The speed of fluid next to the surface of the sphere varies as 1.5 Y0 sin 6, where V0 is the free-stream velocity and 9 is measured from the forward stagnation point. The pressure taps are at the same level; that is, they are in the same horizontal plane. 1he piezometric pressure difference between the two Laps is 2 kPa What is the free-stream velocity Y0?

Explain how you might design a spherical Pitot-static probe to provide the direction and velocity of a flowing stream. The Pitot-static probe will be mounted on a string that can be oriented in any direction.

Two Pitot-static tubes are shown. The one on the top is used to measure the velocity of air, and it is connected to an air-water manometer as shown. The one on the bottom is used to measure the velocity of water, and it too is connected to an air-water manometer as shown. If the deflection h is the same for both manometers, then one can conclude that (a) Y.-~ = Y..,, (b) Y .... > V..,, or (c) YA < Y..,

A Pitot-static tube is used to measure the velocity at the center of a 12 in. pipe. If kerosene at 68F is flowing and the deflection on a mercury-kerosene manometer connected to the Pitot tube is 4 in., what is the velocity?

A Pitot-static tube used to measure air velocity is connected to a differential pressure gage. If the air temperature is 20C at standard atmospheric pressure at sea level, and if the differential gage reads a pressure difference of 2 kPa, what is the air velocity?

A Pilot-static tube used to measure air velocity is connected to a differential pressure gage. If the air temperature is 60F at standard atmospheric pressure at sea level, and if the differential gage reads a pressure difference of 15 psf, what is the air velocity?

A Pilot-static tube is used to measure the gas velocity in a duct. A pressure transducer connected to the Pitot tube registers a pressure difference of 2.0 psi. The density of the gas in the duct is 0.14lbm/ft 3 What is the gas velocity in the duct?

A sphere moves horizontally through still water at a speed of II ft/s. A short distance directly ahead of the sphere (call it point A), the velocity, with respect to the earth, induced by the sphere is 1 ft/s in the same direction as the motion of the sphere. If p0 is the pressure in the undisturbed water at the same depth as the center of the sphere, then the value of the ratio PAip0 will be (a) Jess than unity, (b) equal to unity, or (c) greater than unity.

Body A travels through water at a constant speed of 13 m/s as shown. Velocities at points B and Care induced by the moving body and are observed to have magnitudes of 5 m/s and 3 m/s, respectively. What is Ps - Pc?

Water in a flume is shown for two conditions. if the depth d IS the same for each case, will gage A read greater or less than gage B? Explain.

A rugged instrument used frequently for monitoring gas velocity in smokestacks consists of two open tubes oriented to the flow direction as shown and connected to a manometer. The pressure coefficient is 1.0 at A and - 0.3 at B. Assume that water, at 20C, is used in the manometer and that a 5 mm deflection is noted. The pressure and temperature of the stack gases are I 0 I kPa and 250C. The gas constant of the stack gases is 200 )/kg K. Determine the velocity of the stack gases.

The pressure in the wake of a bluff body is approximately equal to the pressure at the point of separation. The velocity distribution for flow over a sphere is V = 1.5 V0 sin ll, where V0 is the free-stream velocity and 0 is the angle measured from the forward stagnation point. The flow separates at 0 = 120. If the free-stream velocity is 100m/sand the tluid is air (p = 1.2 kglm3 ), find tl1e pressure coefficient in the separated region next to the sphere. Also, what is the gage pressure in this region if the free-stream pressure is atmospheric?

A Pitot-static tube is used to measure the airspeed of an airplane. The Pi tot tube is connected to a pressure-sensing device calibrated to indicate the correct airspeed when the temperature is l7C and the pressure is 101 kPa. The airplaue flies at an altitude of 3000 m, where the pressure and temperature are 70 kPa and -6.3C. The indicated airspeed is 70 m/s. What is the true airspeed?

An aircraft flying at 10,000 feet uses a Pitot-static tube to measure speed. The instrumentation on the aircraft provides the differential pressure as well as the local static pressure and the local temperature. The local static pressure is 9.8 psig, and the air temperature is 25F. The differential pressure is 0.5 psid. Find the speed of the aircraft in mph.

You need to measure air flow velocity. You order a commercially available Pi tot-static tube, and the accompanying instructions state that the airflow velocity is given by {h. v(ft/min) = I096.7,f"d where hv is the "velocity pressure" in inches of water and dis the density in pounds per cubic foot. The velocity pressure is the deflection measured on a water manometer attached to the static and total pressure ports. The instructions also state the density d can be calculated using d (lbm/ft3 ) = 1.325 ~where P" is the barometric pressure in inches of mercury and Tis the absolute temperature in degrees Rankine. Before you use the Pi tot tube you want to confirm that the equations are correct. Determine if they are correct.

Consider the flow of water over the surfaces shown. For each case the depth of water at section D-D is the same ( 1 ft), and the mean velocity is the same and equal to 10 ft/s. Which of the following statements are valid? a. pc;> pB>pA b. Ps > Pc > P11 c. PA = PB = Pc d. PH

What is meant by rotation of a fluid particle? Use a sketch to explain

Consider a spherical fluid particle in an inviscid fluid (no shear stresses).If pressure and gravitational forces are the only forces acting on the particle, can they cause the particle to rotate? Explain

The vector V = I Oxi - I Oyj represents a two-dimensional velocity field. Is the flow irrotational?

The velocity components for a two-dimensional flow are Cx Cy u = v = (/ + x2) (x2 + /) where Cis a constant. Is the flow irrotational?

A two-dimensional flow field is defined by u = x 2 - I and v = - 2xy. Is the flow rotational or irrotational?

Fluid flows between two parallel stationary plates. The distance between the plates is I em. The velocity profile between the two plates is a parabola with a maximum velocity at the centerline of 2 cm/s. The velocity is given by u = 2(1 - 4/) where y is measured from the centerline. The cross-flow component of velocity, v, is zero. There is a reference line located I em downstream. Find an expression, as a function of y, for the amount of rotation (in radian) a fluid particle will undergo when it travels a distance of I em downstream.

A combination of a forced and a free vortex is represented by the velocity distribution I v0 = - [1 - exp(- r 2 )] r For r ~ 0 the velocity approaches a rigid body rotation, and as r becomes large, a free-vortex velocity distribution is approached. Find the amount of rotation (in radians) that a fluid particle will experience in completing one circuit around the center as a function of r. Hint: The rotation rate in a flow with concentric streamlines is given by . dvu Yo I d 20 = +- = --d (vor) dr r r r Evaluate the rotation for r = 0.5, 1.0, and 1.5.

Liquid flows with a free surface around a bend. The liquid is inviscid and incompressible, and the flow is steady and irrotational. The velocity varies with the radius across the flow as V = 1/r m/s, where r is in meters. Find the difference in depth of the liquid from the inside to the outside radius. The inside radius of the bend is I m and the outside radius is 3 m.

The velocity in the outlet pipe from this reservoir is 30 ft!s and h = 18ft. Because of the rounded entrance to the pipe, the flow is assumed to be irrotational. Under these conditions, what is the pressure at A?

The velocity in the outlet pipe from this reservoir is 8 m/s and h = 19 m. Because of the rounded entrance to the pipe, the flow is assumed to be irrotational. Under these conditions, what is the pressure at A?

The maximum velocity of the flow past a circular cylinder, as shown, is twice the approach velocity. What is l:lp between the point of highest pressure and the point of lowest pressure in a 40 m/s wind? Assume irrotational flow and standard atmospheric conditions.

The velocity and pressure are given at two points in the flow field. Assume that the two points lie in a horizontal plane and that the fluid density is uniform in the flow field and is equal to 1000 kg/m3 Assume steady flow. Then, given these data, determine which of the following statements is true. (a) Tile flow ' n the contraction is nonuniform and irrotational. (b) The flow in the contraction is uniform and irrotational. (c) The flow in the contraction is nonuniform and rotational. (d) The flow in the contraction is uniform and rotational.

Ideal flow theory will yield a flow pattern past an -rfoil similar to that shown. If the approach air velocity V0 is ':> m/s, what is the pressure difference between the bottom and ::1e top of this airfoil at points where the velocities are V1 = 85 m/ s ..:~d V2 = 75 m/s? Assume Pair is uniform at 1.2 kg/m3 .

Consider the flow of water between two parallel plates in mch one plate is fixed as shown. The distance between the plates is h, and the speed of the moving plate is V. A person wishes to calculate the pressure difference between the plates and applies the Bernoulli equation between points 1 and 2, p, v [ Pz v~ z1 + - + - = z2 + - + - -y 2g -y 2g and concludes that y l p, - P2 = -y(z2 - z1) + p-2. 2 yl = -yh + p2 Is this correct? Provide the reason for your answer.

Euler's equations for a planar (two-dimensional) flow in the xy-plane are au au ah u - + v- = - g- x = direction ax ay ax av av ilh u- + v- = -g- y =direction ax ay ay a. The slope of a streamline is given by dy v - = dx u Using this relation in Euler's equation, show that ( u2 + vl ) d~+h = 0 or d(~; +h)= 0 which means that V2 /2g + his constant along a streamline. b. For an irrotational flow, au av ay ilx Substituting this equation into Euler's equation, show that a (v2 ) - -+h =0 ax 2g a (v 2 ) ay 2g + h = 0 which means that V2 /2g + h is constant in all directions.

A fluid is flowing arow1d a cylinder as shown in Fig 4.37 on p. 149 in 4.1 0. A favorable pressure gradient can be found a. upstream of the stagnation point b. at the stagnation point c. between the stagnation point and separation point

The velocity distribution over the surface of a sphere upstream of the separation point is Ue = 1.5 U Sin 9, where U is the free stream velocity and 9 is the angle measured from the forward stagnation point. A pressure of -2.5 in H20 gage is measured at the point of separation on a sphere in a 100 ft/s airflow with a density of 0.07lbmtfe. The pressure far upstream of the sphere in atmospheric. Estimate the location of the stagnation point (ll). Separation occurs on the windward side of the sphere.

Knowing the speed at point 1 of a fluid upstream of a sphere and the average speed at point 2 in the wake of in the sphere, can one use the Bernoulli equation to find the pressure difference between the two points? Provide the rationale for your decision.

Take a spoon and rapidly stir a cup of liquid. Report on the contour of the surface. Provide an explanation for the observed shape.

This closed tank, which is 4ft in diameter, is filled with water (p = 62.4 lbm/ft3 ) and is spun around its vertical centroidal axis at a rate of 10 rad!s. An open piezometer is connected to the tank as shown so that it is also rotating with the tank. For these conditions, what is the pressure at the center of the bottom of the tank?

A tank of liquid (S = 0.80) that is 1 ft in diameter and 1.0 ft high (h = l.O ft) is rigidly fixed (as shown) to a rotating arm having a 2 ft radius. The arm rotates such that the speed at point A is 20 ft!s. lf the pressure at A is 25 psf, what is the pressure at B?

A closed tank ofliquid (S = 1.2) is rotated about a vertical axis (see the figure), and at the san1e time the entire tank is accelerated upward at 4 m/s2 . lf the rate of rotation is I 0 rad/s, what is the difference in pressure between points A and 8 (p8 - PA)? Point 8 is at the bottom of the tank at a radius of 0.5 m from the axis of rotation, and point A is at the top on the axis of rotation.

AU-tube is rotated about one leg, as shown. Before being rotated the liquid in the tube fills 0.25 m of each leg. The length of the base of the U-tube is 0.5 m, and each leg is 0.5 m long. What would be the maximum rotation rate (in rad/s) to ensure that no liquid is expelled from the outer leg?

An arm with a stagnation tube on the end is rotated at I 00 rad/s in a horizontal plane I 0 em below a liquid surface as shown. The arm is 20 em long, and the tube at the center of rotation extends above the liquid surface. The liquid in the tube is the same as that in the tank and has a specific weight of I 0,000 N/ m3 . Find the location of the liquid surface in the central tube.

AU-tube is rotated at 50 rev/min about one leg. "!he fluid .at the bottom of the U-tube has a specific gravity of 3.0. The distance between the two legs of the U-tube is I ft. A 6 in. height of another fluid is in the outer leg of the U-tube. Both legs are open to the atmosphere. Calculate the specific gravity of the ther fluid.

A manometer IS rotated around one leg, as shown. :he difference in elevation between the liquid surfaces in the .egs is 20 em. The radius of the rotating arm is 10 em. The liquid -o the manometer is oil with a specific gravity of 0.8. Find the "':umber of g's of acceleration in the leg with greatest amount .>foil.

A fuel tank for a rocket in space under a zero-g environment is rotated to keep the fuel in one end of the tank. The system is rotated at 3 rev/min. The end of the tank (point A) is 1.5 m from the axis of rotation, and the fuel level is 1 rn from the rotation axis. The pressure in the nonliquid end of the tank is 0.1 kPa, and the density of the fuel is 800 kg/m3 What is the pressure at the exit (point A)?

Water stands in these tubes as shown when no rotation occurs. Derive a formula for the angular speed at which water will just begin to spill out of the small tube when the entire system is rotated about axis A-A.

Water (p = 1000 kg/m3 ) fills a slender tube 1 em in diameter, 40 em long, and closed at one end. When the tube is rotated in the horizontal plane about its open end at a constant speed of 50 rad/s, what force is exerted on the closed end?

Water (p = 1000 kglrn3 ) stands in the closed-end U-tube as shown when there is no rotation. [f e = 2 em and if the entire system is rotated about axis A-A, at what angular speed will water just begin to spill out of the open tube? Assume that the temperature for the system is the same before and after rotation and that the pressure in the closed end is initially atmospheric.

A closed cylindrical tank of water (p = 1000 kg/m3 ) is rotated about its horizontal axis as shown. The water inside the tank rotates with the tank (V = rw). Derive an equation for dpldz along a vertical-radialline through the center of rotation. What is dpldz along this line for z = -1m, z = 0, and z = + 1 m when w = 5 rad/s? Here z = 0 at the axis.

The tank shown is 4 ft in diameter and I 2 ft long and is closed and filled with water (p = 62.4lbm/ft3). It is rotated about its horizontalcentroidal axis. and the water in the tank rotates with the tank (V = rw). The maximum velocity is 25 ft/s. What is the maximum difference in pressure in the tank? Where is the point of minimum pressure?