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Problems in Chapter 5 (Control Volume Analysis)
1. Incompressible, laminar water flow develops in a straight pipe having
radius R as indicated in Figure. At section (1), the velocity profile is
uniform; the velocity is equal to a constant value U and is parallel to the
pipe axis everywhere. At section (2), the velocity profile is axisymmetric
and parabolic, with zero velocity at the pipe wall and a maximum value of
umax at the centerline. How are U and umax related? How are the average
velocity at section (2), V2 and umax related?
Sol) Ú Relevant principle: The Continuity Equation
∂
ρdV +
∂t ∫CV
∫CS
r
ρV ⋅ nˆ dA = 0
(Steady flow)
2. Water flows through a horizontal, 180o pipe bend as illustrated in Figure.
The flow cross-sectional area is constant at a value of 0.1 ft2 through the
bend. The flow velocity everywhere in the bend is axial and 50 ft/s. The
absolute pressures at the entrance and exit of the bend are 30 psia and 24
psia, respectively. Calculate the horizontal (x and y) components of the
anchoring force required to hold the bend in place.
3. Water flows through a horizontal bend and discharges into the atmosphere
as shown in Figure. When the pressure gage reads 10 psi, the resultant x
direction anchoring force, in the horizontal plane required to hold the bend in
place is shown on the figure. Determine the flowrate through the bend and
the y direction anchoring force, required to hold the bend in place. The flow
is not frictionless.
4. The pump shown in Figure adds 20 kW of power to the flowing water.
The only loss is that which occurs across the filter at the inlet of the pump.
Determine the head loss for this filter.
in
out
5. What is the maximum possible power output of the hydroelectric turbine
shown in Figure?