Problem set Five
1) A circular plate having a diameter of 300 mm is held perpendicular to an axisymmetric
horizontal jet of air having a velocity of 40 m/s and a diameter of 80 mm as shown in Fig.
5-1. A hole at the center of the plate results in a discharge jet of air having a velocity of
40 m/s and a diameter of 20 mm. Determine the horizontal component of force required
to hold the plate stationary.
Figure 5-1 Horizontal jet
F  9.27 N  9.27 N 
2) A horizontal, circular cross-sectional jet of air having a diameter of 6 in, strikes a
conical deflector as shown in Fig. 5-2. A horizontal anchoring force of 5 lb is required to
hold the cone in place. Estimate the nozzle flowrate in ft3/s. the magnitude of the velocity
of the air remains constant. Angle 60º, ρair = 0.00238 slug/ft3
Figure 5-2 A conical reflector
Q
2  Fax  A



6
 ( ) 2 ft 2
4 12
 28.72 ft 3 /s
3
0.00238 slug/ft
2  5 lbf 
3) An airplane moves forward with a steady airspeed of 250 km/hr. The wings of this
plane deflect the air flow around each wing downward by an angle of 10º. Estimate the
mass flowrate of the deflected air required over the wing surfaces if the mass of the plane
and its contents is 3000 kg. Assume that air leaves the wing at the same speed it entered
with and consider momentum change effects only.
(1)
o
10
Fy
(2)
m
F
Vwing

29430 N
 2440.30 kg/s
12.06 m/s
y
x
4) A vertical jet of water leaves a nozzle at a speed of 10 m/s and a diameter of 20 mm. It
suspends a plate having a mass of 1.5 kg as indicated in Fig. 5-4. What is the vertical
distance h?
Figure 5-4 A vertical jet.
h
(Vo2  V12 ) (102 -4.682 ) m2 /s 2

 3.98 m
2 g
2×9.81 m/s 2
5.) Exhaust (assumed to have the properties of standard air) leaves the 4 ft diameter
chimney shown in Fig. 5-5 with speed of 6 ft/s. Because of the wind, after a few
diameters downstream the exhaust flows in a horizontal direction with the speed of the
wind, 15 ft/s. Determine the horizontal component of the force that the blowing wind puts
on the exhaust gases.
Figure 5-5 Exhaust through a chimney.
Rx  m2 V2  0.179 slug/s×15 ft/s=2.69 lbf
6) Oil (SG = 0.9) flows downward through a vertical pipe contraction as shown in Fig. 56. If the mercury manometer reading, h, is 100 mm, determine the volume flowrate for
frictionless flow. Is the actual flowrate more or less than the frictionless value? Explain.
D1 = 300 mm, height 0.6 m, D2 = 100 mm.
Figure 5-6 Oil through vertical pipe
Q  A2V2  5.29 m/s×0.00785 m 2 =0.0416 m3 /s
Actual flow rate is less since velocity is smaller with friction in the pipe.
7) A water siphon having a constant inside diameter of 3 in is arranged as shown in Fig.
5-7. If the friction loss between A and B is 0.8 V2/2, where V is the velocity of flow in the
siphon, determine the flowrate involved.
Figure 5-7 A water siphon
Q  A  V2  0.049 ft 2 ×16.92 ft/s=0.829 ft 3 /s
8) A fire hose nozzle is designed to deliver water that will rise 40 m vertically. Calculate
the stagnation pressure required at the nozzle inlet if (a) no loss is assumed, (b) a loss of
30 N m/kg is assumed.
a)  gz1  P2  1000 kg×9.81 m/s 2 ×40 m = 392400 Pa = 392.4 kPa
Add the loss to the stagnation pressure found in part a. this gives the actual pressure
taking inconsideration the losses.
b) P  P2  loss = 392.4 kPa + 30 kPa = 422.4 kPa