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Problem 3.113
An airplane is flying at 300 mi/h at 4000 m standard altitude. As is typical, the air velocity
relative to the upper surface of the wing, near its maximum thickness, is 26 percent higher than
the plane’s velocity. Using Bernoulli’s equation, calculate the absolute pressure at this point on
the wing. Neglect elevation changes and compressibility.
Solution 3.113
Fix the frame of steady flow relative to
Problem 3.114
Water flows through a circular nozzle, exits into the air as a jet, and strikes a plate, as shown in
Fig. P3.114. The force required to hold the plate steady is 70 N. Assuming steady, frictionless,
one-dimensional flow, estimate ( a ) the velocities at sections (1) and (2) and ( b ) the mercury
manometer reading h .
1.26 Uo
Solution 3.114
(a) First examine the momentum of the jet striking the plate,
2
22in in
F F m u A V
= = − = −
Problem 3.115
A free liquid jet, as in Fig. P3.115, has constant ambient pressure and small losses; hence from
Bernoulli’s equation z + V2/(2g) is constant along the jet. For the fire nozzle in the figure, what
are (a) the minimum and (b) the maximum values of
for which the water jet will clear the
corner of the building? For which case will the jet velocity be higher when it strikes the roof of
the building?
Solution 3.115
The two extreme cases are when the jet just touches the corner A of the building. For these two
cases, Bernoulli’s equation requires that
Problem 3.116
For the container of Fig. P3.116 use Bernoulli’s equation to derive a formula for the distance X
where the free jet leaving horizontally will strike the floor, as a function of h and H. For what
ratio h/H will X be maximum? Sketch the three trajectories for h/H = 0.25, 0.5, and 0.75.
Solution 3.116
The velocity out the hole and the time to fall from hole to ground are given by
Problem 3.117
Water at 20C, in the pressurized tank of Fig. P3.117, flows out and creates a vertical jet as
shown. Assuming steady frictionless flow, determine the height H to which the jet rises.
Solution 3.117
This is a straightforward Bernoulli problem. Let the water surface
be (1), the exit plane be (2), and the top of the vertical jet be (3). Let z2 = 0 for convenience.
If we are clever, we can bypass (2) and write Bernoulli directly from (1) to (3):
Problem 3.118
Bernoulli’s 1738 treatise Hydrodynamica contains many excellent sketches of flow patterns
related to his frictionless relation. One, however, redrawn here as Fig. P3.118, seems physically
misleading. Can you explain what might be wrong with the figure?
Solution 3.118
If friction is neglected and the exit pipe is fully open, then pressure in the closed “piezometer”
tube would be atmospheric and the fluid would not rise at all in the tube. The open jet coming
from the hole in the tube would have V (2gh) and would rise up to nearly the same height as
the water in the tank.
Fig. P3.118
Problem 3.119
A long fixed tube with a rounded nose, aligned with an oncoming flow, can be used to measure
velocity. Measurements are made of the pressure at (1) the front nose and (2) a hole in the side of
the tube further along, where the pressure nearly equals stream pressure. (a) Make a sketch of
this device and show how the velocity is calculated. (b) For a particular sea-level airflow, the
difference between nose pressure and side pressure is 1.5 lbf/in2 . What is the air velocity, in
mi/h?
Solution 3.119
(a) The front nose measures po
Problem 3.120
The manometer fluid in Fig. P3.120 is mercury. Estimate the volume flow in the tube if the
flowing fluid is (a) gasoline and (b) nitrogen, at 20°C and 1 atm.
Solution 3.120
For gasoline (a) take
= 1.32 slug/ft3. For nitrogen (b), R 297 J/kg °C and
Problem 3.121
In Fig. P3.121 the flowing fluid is CO2 at 20°C. Neglect losses. If p1 = 170 kPa and the manometer
fluid is Meriam red oil (SG = 0.827), estimate (a) p2 and (b) the gas flow rate in m3/h.
Solution 3.121
Estimate the CO2 density as
= p/RT = (170000)/[189(293)] 3.07 kg/m3. The manometer
reading gives the down-stream pressure:
Problem 3.122
The cylindrical water tank in Fig. P3.122 is being filled at a volume flow Q1 = 1.0 gal/min, while
the water also drains from a bottom hole of diameter d =6 mm. At time t = 0, h = 0. Find (a) an
expression for h(t) and (b) the eventual maximum water depth hmax. Assume that Bernoulli’s
steady-flow equation is valid.
Solution 3.122
Bernoulli predicts that V2 (2gh).
Problem 3.123
The air-cushion vehicle in Fig. P3.123 brings in sea-level standard air through a fan and
discharges it at high velocity through an annular skirt of 3-cm clearance. If the vehicle weighs
50 kN, estimate (a) the required airflow rate and (b) the fan power in kW.
Solution 3.123
The air inside at section 1 is nearly stagnant (V 0) and supports the weight and also drives the
flow out of the interior into the atmosphere:
Then the power required by the fan is P = Qep = (30.6)(1768) 54000 W Ans.
Problem 3.124
A necked-down section in a pipe flow, called a venturi, develops a low throat pressure that can
aspirate fluid upward from a reservoir, as in Fig. P3.124. Using Bernoulli’s equation with no
losses, derive an expression for the velocity V1 that is just sufficient to bring reservoir fluid into
the throat.
Solution 3.124
Water will begin to aspirate into the throat when pa − p1 =
gh. Hence:
Problem 3.125
Suppose you are designing an air hockey table. The table is 3.0 × 6.0 ft in area, with
1
16
-in-
diameter holes spaced every inch in a rectangular grid pattern (2592 holes total). The required jet
speed from each hole is estimated to be 50 ft/s. Your job is to select an appropriate blower that
Problem 3.126
The liquid in Fig. P3.126 is kerosene at 20°C. Estimate the flow rate from the tank for (a) no
losses and (b) pipe losses hf 4.5V2/(2g).
Solution 3.126
Problem 3.127
In Fig. P3.127 the open jet of water at 20°C exits a nozzle into sea-level air and strikes a
stagnation tube as shown. If the pressure at the centerline at section 1 is 110 kPa, and losses are
neglected, estimate (a) the mass flow in kg/s and (b) the height H of the fluid in the stagnation
tube.
Solution 3.127
