fluid_mechanics

Problems 261
24 in. 40 ft/s
F I G U R E P5.124
p 1 p 2 , (b) the loss between sections 112 and 122, (c) the net axial
force exerted by the pipe wall on the flowing water between sections
112 and 122.
5.128 Water flows steadily in a pipe and exits as a free jet through
an end cap that contains a filter as shown in Fig. P5.128. The flow
is in a horizontal plane. The axial component, R y , of the anchoring
force needed to keep the end cap stationary is 60 lb. Determine the
head loss for the flow through the end cap.
2-m-dia.
Air
Wake 1-m dia.
4 m/s
Area = 0.10 ft 2
R y = 60 lb
12 m/s
R x
p = 50 N/m 2
V = 10 m/s
F I G U R E P5.125
pipe exit the velocity is nonuniform as indicated. The shear stress
along the pipe wall is negligible. (a) Determine the head loss associated
with a particle as it flows from the uniform velocity upstream
of the object to a location in the wake at the exit plane of the pipe.
(b) Determine the force that the air puts on the object.
5.126 Water flows through a 2-ft-diameter pipe arranged horizontally
in a circular arc as shown in Fig. P5.126. If the pipe discharges
to the atmosphere (p 14.7 psia) determine the x and y components
of the resultant force exerted by the water on the piping between
sections (1) and (2). The steady flowrate is 3000 ft 3 /min. The loss in
pressure due to fluid friction between sections (1) and (2) is 60 psi.
y
Exit
30°
Area = 0.12 ft 2
F I G U R E P5.128
V = 10 ft/s
Filter
Pipe
5.129 When fluid flows through an abrupt expansion as indicated
in Fig. P5.129, the loss in available energy across the expansion,
loss ex , is often expressed as
loss ex a1 A 2
1 V 2 1
b
A 2 2
where A 1 cross-sectional area upstream of expansion, A 2
cross-sectional area downstream of expansion, and V 1 velocity
of flow upstream of expansion. Derive this relationship.
90°
1000 ft
x
Section (2)
Section (1)
Flow
F I G U R E P5.126
5.127 Water flows steadily down the inclined pipe as indicated in
Fig. P5.127. Determine the following: (a) the difference in pressure
Section (1)
Section (2)
F I G U R E P5.129
Flow
Section (1)
6 in.
5 ft
5.130 Two water jets collide and form one homogeneous jet as
shown in Fig. P5.130. (a) Determine the speed, V, and direction, u,
of the combined jet. (b) Determine the loss for a fluid particle flowing
from 112 to 132, from 122 to 132. Gravity is negligible.
30°
Section (2)
0.12 m
(3)
V
V 2 = 6 m/s
θ
6 in.
(2)
90°
(1)
0.10 m
F I G U R E P5.127
Mercury
V 1 = 4 m/s
F I G U R E P5.130