fluid_mechanics

Problems 251
5.47 A converging elbow (see Fig. P5.47) turns water through an
angle of 135° in a vertical plane. The flow cross section diameter is
400 mm at the elbow inlet, section (1), and 200 mm at the elbow outlet,
section (2). The elbow flow passage volume is 0.2 m 3 between
sections (1) and (2). The water volume flowrate is 0.4 m 3 s and the
elbow inlet and outlet pressures are 150 kPa and 90 kPa. The elbow
mass is 12 kg. Calculate the horizontal (x direction) and vertical
(z direction) anchoring forces required to hold the elbow in place.
place. Estimate the nozzle flowrate in ft 3 s. The magnitude of the
velocity of the air remains constant.
5.51 A vertical, circular cross-sectional jet of air strikes a conical deflector
as indicated in Fig. P5.51. A vertical anchoring force of 0.1 N
is required to hold the deflector in place. Determine the mass 1kg2 of
the deflector. The magnitude of velocity of the air remains constant.
F A = 0.1 N
z
Section
(1)
D 1 = 400 mm
135°
x
60°
0.1 m
D 2 =
200 mm
F I G U R E P5.47
Section (2)
5.48 The hydraulic dredge shown in Fig. P5.48 is used to dredge
sand from a river bottom. Estimate the thrust needed from the propeller
to hold the boat stationary. Assume the specific gravity of the
sandwater mixture is SG 1.2.
V = 30 m/s
F I G U R E P5.51
5.52 Water flows from a large tank into a dish as shown in Fig.
P5.52. (a) If at the instant shown the tank and the water in it
weigh W 1 lb, what is the tension, T 1 , in the cable supporting the
tank? (b) If at the instant shown the dish and the water in it weigh
W 2 lb, what is the force, F 2 , needed to support the dish?
T 1
30 ft/s
2-ft diameter
30°
10 ft
Tank
9 ft 7 ft Prop
F I G U R E P5.48
0.1-ft diameter
12 ft
5.49 A static thrust stand is to be designed for testing a specific jet
engine. Knowing the following conditions for a typical test,
intake air velocity 700 fts
exhaust gas velocity 1640 fts
intake cross section area 10 ft 2
intake static pressure 11.4 psia
intake static temperature 480 °R
exhaust gas pressure 0 psi
estimate a nominal thrust to design for.
5.50 A horizontal, circular cross-sectional jet of air having a diameter
of 6 in. strikes a conical deflector as shown in Fig. P5.50.
A horizontal anchoring force of 5 lb is required to hold the cone in
2 ft
Dish
F 2
F I G U R E P5.52
5.53 Two water jets of equal size and speed strike each other as
shown in Fig. P5.53. Determine the speed, V, and direction, u, of
the resulting combined jet. Gravity is negligible.
V
θ
V 2 = 10 ft /s
0.1 ft
60° F A = 5 lb
6 in.
90°
0.1 ft
V 1 =10 ft /s
F I G U R E P5.50
F I G U R E P5.53