2. The forces (F1and F2)are each about 40 lbf. This magnitude of force may be
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6.15: PROBLEM DEFINITION
Situation:
Water jet f rom a fire hose on a boat.
d=4in,V=60mph = 88.0ft/s.
Find:
Tensionincable(lbf).
Sketch:
Properties:
Water (50 ◦F), Table A.5: ρ=1.94 slug/ft3.
PLAN
Apply the momentum equation.
SOLUTION
Force and momentum diagrams
Flow rate
Momentum equation (x-direction)
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6.16: PROBLEM DEFINITION
Situation:
Water jet f rom a fire hose on a boat.
T=5.0kN, v=50m/s.
Find:
Mass flow rate of jet (kg/s).
Diameter of jet (cm).
Sketch:
Properties:
Water (5◦C), Table A.5: ρ=1000kg/m3.
PLAN
Apply the momentum equation to find the mass flow rate. Then, calculate diameter
using the flow rate equation.
SOLUTION
Force and momentum diagrams
Momentum equation (x-direction)
Flow rate
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24
6.17: PROBLEM DEFINITION
Situation:
Piston water guns used to shoot water from one raft to another.
After volleys, rafts are drifting apart.
Water is ejected from piston water gun at a flow rate of 1 gal/s.
Diameter of gun exit is 1.5 in.
Find:
The momentum flux (N) generated by ejecting water from a water gun.
PLAN
a. SketchaCV,aFDandaMDaspreparationforemployingthemomentum
equation.
b. Employ the momentum equation (also called the Impulse-Momentum Eqn).
SOLUTION
a. SketchaCV,aFDandaMD.
b. Employ the Linear Momentum Equation.
Determine the velocity of the jet
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Using the FD and the MD, we set up the following equation, where F = force of
the person compressing the piston.
6.18: PROBLEM DEFINITION
Situation:
Pressurized air drives a water jet out of a tank. The thrust of the water jet reduces
the tension in a supporting cable.
W= 200 N,T=10N.
d=12mm,H=425mm.
Find:
The pressure in the air that is situated above the water.
Sketch:
Pressurized Air
Water
H
Vertical Cable
Jet–diameter d
Assumptions:
Assume that the Bernoulli equation can be applied (i.e. assume irrotational and
steady flow).
Properties:
Water (15 ◦C), Table A.5: ρ=999kg/m3.
PLAN
Apply the momentum equation to find the exit velocity. Then, apply the Bernoulli
equation to find the pressure in the air.
SOLUTION
Section area of jet
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Momentum equation (cv surrounding the tank; section 2 at the nozzle)
Bernoulli equation (location 1 is on the water surface, location 2 is at the water jet).
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6.19: PROBLEM DEFINITION
Situation:
Free water jet from upper tank to lower tank, lower tank supported by scales A
and B.
Find:
Force on scale A (lbf).
Force on scale B (lbf).
Sketch:
Properties:
Water (60 oF): ρ=1.94 slug/ft3,γ=62.4lbf/ft3.
PLAN
Apply the momentum equation.
SOLUTION
Force and momentum diagrams
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Flow rate
Projectile motion equations
Momentum equation (x-direction)
Momentum equation (y-direction)
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6.20: PROBLEM DEFINITION
Situation:
Gravel flows into a barge that is secured with a hawser.
Q=50yd3/min = 22.5 ft3/s, v=10ft/s.
Find:
Tensioninhawser: T
Sketch:
Assumptions:
Steady flow.
Properties:
γ=120lbf/ft3
PLAN
Apply the momentum equation.
SOLUTION
Force and momentum diagrams
Momentum equation (x-direction)
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6.21: PROBLEM DEFINITION
Situation:
A hemispherical nozzle sprays a sheet of liquid through an arc.
Find:
An expression for the force in y-direction to hold the nozzle stationary.
Fy=Fy(ρ, v, r, t).
Sketch:
v
y
d
θ
θ
PLAN
Apply the momentum equation.
SOLUTION
Momentum equation (y-direction)
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6.22: PROBLEM DEFINITION
Situation:
The design of a conical rocket nozzle.
Find:
Show that T=˙mVe1+cos α
2.
PLAN
Apply the momentum equation.
SOLUTION
Momentum equation (x-direction)
Exit Area
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6.23: PROBLEM DEFINITION
Q=0.15 m3/s, S=0.9.
Find:
Components of force to hold vane stationary (kN).
Sketch:
PLAN
Apply the momentum equation.
SOLUTION
Force and momentum diagrams
Mass flow rate
Momentum equation (x-direction)
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Momentum equation (y-direction)
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6.24: PROBLEM DEFINITION
Situation:
Afixed vane in the horizontal plane.
v1=70ft/s, v2=65ft/s.
Q=1.5cfs, S=0.9.
Find:
Components of force to hold vane stationary (lbf).
Sketch:
PLAN
Apply the momentum equation.
SOLUTION
Force and momentum diagrams
Momentum equation (x-direction)
y-direction
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6.25: PROBLEM DEFINITION
Situation:
A horizontal, two-dimensional water jet deflected by a fixed vane.
v1=40ft/s, w2=0.2ft, w3=0.1ft.
Find:
Components of force, per foot of width, to hold the vane stationary (lbf/ft).
Assumptions:
Neglect elevation changes.
Neglect viscous effects.
Properties:
Water, Table A.5: ρ=1.94 slug/ft3.
PLAN
Apply the Bernoulli equation, the continuity equation, and finally the momentum
equation.
SOLUTION
Force and momentum diagrams
Continuity equation
Momentum equation (x-direction)
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Momentum equation (y-direction)
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6.26: PROBLEM DEFINITION
Situation:
Awaterjetisdeflected by a fixed vane.
v1=30ft/s, ˙m=35lbm/s = 1.086 slug/s.
Find:
Force of the water on the vane (lbf).
Sketch:
PLAN
Apply the Bernoulli equation, and then the momentum equation.
SOLUTION
Force and momentum diagrams
Momentum equation (x-direction)
y-direction
Since the forces acting on the vane represent a state of equilibrium, the force of water
onthevaneisequalinmagnitude&oppositeindirection.
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