6.54: PROBLEM DEFINITION
Situation:
An unusual nozzle creates two jets of water.
d=0.5in,v
2=v3=80.2ft/s.
D=3.5in.p =50psig.
Find:
Force required at the flange to hold the nozzle in place: F
PLAN
Apply the continuity equation, then the momentum equation.
SOLUTION
Continuity equation
Momentum equation (x-direction)
Momentum equation (y-direction)
81
6.55: PROBLEM DEFINITION
Situation:
Liquid flows through a ”black sphere”–additional details are provided in the prob-
lem statement.
v
2
y
x
v
1
v
3
30
o
Find:
Force in the inlet pipe wall required to hold sphere stationary: F
PLAN
Apply the continuity equation, then the momentum equation.
SOLUTION
Continuity equation
Momentum equation (x-direction)
y-direction
82
Calculations
thus,
83
6.56: PROBLEM DEFINITION
Situation:
Liquid flows through a ”black sphere”–additional details are provided in the prob-
lem statement.
Find:
Force required in the pipe wall to hold the sphere in place: F
PLAN
Apply the continuity equation, then the momentum equation.
SOLUTION
Continuity equation
Momentum equation (x-direction)
Momentum equation (y-direction)
84
6.57: PROBLEM DEFINITION
Situation:
Hot gas flows through a return bend–additional details are provided in the problem
statement.
Find:
Force required to hold the bend in place: Fx
PLAN
Apply the continuity equation, then the momentum equation.
SOLUTION
At section (1):
v1=100ft/s
ρ1=0.02 lbm/ft3=0.000621 slugs/ft3
At section (2):
Continuity equation
Momentum equation (x-direction)
85
6.58: PROBLEM DEFINITION
Situation:
Fluid (density ρ, discharge Q,andvelocityV)flows through a 180opipe bend–
additional details are provided in the problem statement.. Cross sectional area of
pipe is A.
Find:
Magnitude of force required at flanges to hold the bend in place.
Assumptions:
Gage pressure is same at sections 1 and 2. Neglect gravity.
PLAN
Apply the momentum equation.
SOLUTION
Momentum equation (x-direction)
thus
87
6.59: PROBLEM DEFINITION
Situation:
Water flows through a 180opipe bend–additional details are provided in the
problem statement.
Find:
External force required to hold bend in place.
PLAN
Apply the momentum equation.
SOLUTION
Flow rate equation
thus
Momentum equation (y-direction)
88
6.60: PROBLEM DEFINITION
Situation:
Water flows through a 180◦pipe bend–additional details are provided in the
problem statement.
Find:
Forcethatactsontheflanges to hold the bend in place.
PLAN
Apply the continuity and momentum equations.
SOLUTION
Flow rate
Continuity. Place a control volume around the pipe bend. Let section 2 be the exit
and section 1 be the inlet
Momentum equation (x-direction). Place a control volume around the pipe bend.
Let section 2 be the exit and section 1 be the inlet.
Calculations
89
Momentum equation (z-direction). There are no momentum flow terms so the mo–
mentum equation simplifies to
90
6.61: PROBLEM DEFINITION
Situation:
Set up the solution for the preceeding problem, and answer the following questions:
Find:
a. Do the 2 pressure forces from the inlet and exit act in the same direction, or in
opposite directions?
b. For the data given, which term has the larger magnitude (in N), the pressure
force term, or the net momentum flux term?
SOLUTION
a. The 2 pressure forces acting on the inlet and the exit are both acting compres-
91
6.62: PROBLEM DEFINITION
Situation:
A90
◦pipe bend is described in the problem statement.
Find:
Force on the upstream flange to hold the bend in place.
PLAN
Apply the momentum equation.
SOLUTION
Velocity calculation
Momentum equation (x-direction)
y-direction
z–direction
92
6.63: PROBLEM DEFINITION
Situation:
A90
0pipe bend is described in the problem statement.
Find:
x−component of force applied to bend to hold it in place: Fx
PLAN
Apply the momentum equation.
SOLUTION
Momentum equation (x-direction)
93
6.64: PROBLEM DEFINITION
Situation:
Water flows through a 30opipe bend–additional details are provided in the problem
statement.
Find:
Vertical component of force exerted by the anchor on the bend: Fa
PLAN
Apply the momentum equation.
SOLUTION
Velocity calculation
Momentum equation (y-direction)
94
6.65: PROBLEM DEFINITION
Situation:
Water flows through a 60opipe bend and jets out to atmosphere–additional details
are provided in the problem statement.
Find:
Magnitude and direction of external force components to hold bend in place.
PLAN
Apply the Bernoulli equation, then the momentum equation.
SOLUTION
Flow rate equation
Bernoulli equation
Momentum equation (x-direction)
y-direction
z-direction
95
6.66: PROBLEM DEFINITION
Situation:
Water flows through a nozzle–additional details are provided in the problem state-
ment.
Find:
Vertical force applied to the nozzle at the flange: Fy
PLAN
Apply the continuity equation, then the Bernoulli equation, and then the momentum
equation.
SOLUTION
Continuity equation
Bernoulli equation
Momentum equation (y-direction)
Momentum flow terms
Thus, Eq. (1) becomes
96
6.67: PROBLEM DEFINITION
Situation:
Gasoline flows through a 135opipe bend–additional details are provided in the
problem statement.
Find:
External force required to hold the bend: F
PLAN
Apply the momentum equation.
SOLUTION
1
y
x
Flow rate
Momentum equation (x-direction)
Momentum equation (y-direction)
97
98
6.68: PROBLEM DEFINITION
Situation:
A180
opipe bend (6 in. diameter) carries water.
Q=2cfs,p=20psi gage
Find:
Force needed to hold the bend in place: Fx(the component of force in the direction
parallel to the inlet flow)
Assumptions:
The weight acts perpendicular to the flow direction; the pressure is constant
throughout the bend.
PLAN
Apply the momentum equation.
SOLUTION Momentum equation (x-direction)
Calculations
99
6.69: PROBLEM DEFINITION
Situation:
Gasoline flows through a 135opipe bend–additional details are provided in the
problem statement.
Find:
External force required to hold the bend in place: F
PLAN
Apply the momentum equation.
SOLUTION
Discharge
Momentum equation (x-direction)
Momentum equation y-direction
100