5.1 A two-dimensional object is placed in a 4-ft-wide water tunnel as shown. The upstream velocity, υ1 is uniform across the cross section. For the downstream velocity profile as shown, find the value of υ2....
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5.2 A stationary jet engine is shown. Air with a density of 0.0805 lb/ft3 enters as shown. The inlet and outlet cross- sectional areas are both 10.8 ft2.
The mass of fuel consumed is 2% of the mass of air entering the test
section. For these conditions, calculate the thrust developed by the
engine tested....
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5.3 a. Determine the magnitude of the x and y components of the force exerted on the fixed blade shown by a 3-ft3/s jet of water flowing at 25 fps.
b. If the blade is moving to the right at 15 fps, find the magnitude and velocity of the water jet leaving the blade....
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5.4 The pump in the boat shown pumps 6 ft3/s of water through a submerged water passage, which has an area of 0.25 ft2 at the bow of the boat and 0.15 ft2 at the stern. Determine the tension in the restraining rope, assuming that the inlet and exit pressures are equal....
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5.5 At the end of a water pipe of 3-in. diameter is a nozzle that discharges a jet having a diameter of ...
in into the open atmosphere. The pressure in the pipe is 60 psig
(pounds per square inch gage), and the rate of discharge is 400 gal/min.
What are the magnitude and direction of the force necessary to hold the
nozzle to the pipe?
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5.6 If the plate shown is inclined at an angle as shown, what are the forces Fxand Fy necessary to maintain its position? The flow is frictionless....
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5.7 A plate moves perpendicularly toward a discharging jet at the rate of 5 fps. The jet discharges water at the rate of 3 ft3/s
and a speed of 30 fps. Find the force of the fluid on the plate and
compare it with what it would be if the plate were stationary. Assume
frictionless flow.
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5.8 The shock wave illustrated below is moving to the right at υw
fps. The properties in front and in back of the shock are not a
function of time. By using the illustrated control volume, show that the
pressure difference across the shock is...
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5.9 Water
flows steadily through the horizontal 30° pipe bend shown below. At
station 1, the diameter is 0.3 m, the velocity is 12 m/s, and the
pressure is 128 kPa gage. At station 2, the diameter is 0.38 m and the pressure is 145 kPa gage. Determine the forces Fx and Fz necessary to hold the pipe bend stationary....
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5.10 The pressure on the control volume illustrated below is constant. The x
components of velocity are as illustrated. Determine the force exerted
on the cylinder by the fluid. Assume incompressible flow....
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5.11 Adamdischarge
into a channel of constant width as shown. It is observed that a region
of still water backs up behind the jet to a height H. The velocity and height of the flow in the channel are given as υ and h, respectively, and the density of the water is r. Using the momentum theorem and the control surface indicted, determine H.
Neglect the horizontal momentum of the flow that is entering the
control volume from above, and assume friction to be negligible. The air
pressure in the cavity below the crest of falling water is to be taken
as atmospheric....
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5.12 As can often be seen in a kitchen sink when the faucet is running, a high-speed channel flow (υ1, h1) may “jump” to a low-speed, low-energy condition (υ2, h2).
The pressure at sections 1 and 2 is approximately hydrostatic, and wall
friction is negligible. Use the continuity and momentum relations to
find h2 and υ2 in terms of (h1,υ1)....
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5.13 An
open tank car as shown travels to the right at a uniform velocity of
4.5 m/s. At the instant shown the car passes under a jet of water
issuing from a stationary 0.1-m-diameter pipe with a velocity of 20 m/s.
What force is exerted on the tank by the water jet?...
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5.14 liquid column of height h is confined in a vertical tube of cross-sectional area A by a stopper. At t
= 0, the stopper is suddenly removed, exposing the bottom of the liquid
to atmospheric pressure. Using a control-volume analysis of mass and
vertical momentum, derive the differential equation for the downward
motion v (t) of the liquid. Assume one-dimensional, incompressible, frictionless flow....
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5.15 Sea water, ρ = 64 lbm/ft3,
flows through the impeller of a centrifugal pump at the rate of 800
gal/min. Determine the torque exerted on the impeller by the fluid and
the power required to drive the pump. Assume that the absolute
velocity of the water entering the impeller is radial. The dimensions
are as follows:...
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5.16 A
lawn sprinkler consists of two sections of curved pipe rotating about a
vertical axis as shown. The sprinkler rotates with an angular velocity w, and the effective discharge area is A, the water is discharged at a rate Q = 2vPrA, where vr is the velocity of the water relative to the rotating pipe. A constant friction torque Mf
resists the motion of the sprinkler. Find an expression for the speed
of the sprinkler in terms of the significant variables....
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5.17 Water flows at 30 gal/min through the 0.75-in.-diameter double-pipe bend. The pressures are p1 = 30 lbf/in.2 and p2 = 24 lbf/in.2. Compute the torque T at point B necessary to keep the pipe from rotating....
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5.18 You
have been given a project where you must attach a particular reducing
pipe fitting into a Freon-12 delivery system. Freon-12 is a potentially
hazardous material so you must be certain that the reducing pipe fitting
is attached properly and will withstand the force due to the reduction
in pipe diameter. The direction of the flow and the inlet and outlet
positions are labeled in the figure below. The inlet has a diameter of 1
ft, and a pressure of 1000 lbf/ft2. The outlet port has a diameter of 0.2 ft and a pressure of 200 lbf/ft2. The system must maintain a constant flow rate of 4.5 ft3/s and constant temperature of 80°F. The weight of the Freon in the fitting is 6 lbf.
In your analysis you may assume that the system is at steady state and
that the fluid is incompressible. Please calculate the forces in all
directions necessary to hold the fitting stationary....
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5.19 Water
at 100°C flows through a 10 cm diameter pipe that has a 180 degree
vertical turn as shown in the figure below. The volumetric flow rate is
constant at 0.2 m3/s. The absolute pressure at
position 1 is 64,000 Pa, and the absolute pressure at position 2 is
33,000 Pa. The weight of the fluid and pipe together is 10 kg. Please
calculate the total force that vertical turn must withstand to remain in
place assuming the system is at steady state....
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5.20 A water jet at 60°F with a flow rate of 250 ft3/s
and a velocity of 75 ft/s hits a stationary V-shaped splitter such that
half of the fluid is directed upward and the other half is directed
downward as shown in the figure. Both of these streams have a final
velocity of 75 ft/s. Assume steady, incompressible flow, that
gravitational effects are negligible, and that the entire system is open
to the atmosphere where the pressure is 2116.8 lbf/ft2. Please calculate the x and y components of force required to hold the V-shaped splitter in place....
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