7.83: PROBLEM DEFINITION
Situation:
A reservoir discharges into a pipe.
Find:
Draw the HGL and EGL.
SOLUTION
120
7.84: PROBLEM DEFINITION
Situation:
Water discharges through a turbine.
Q=1000cfs, η=85%.
hL=4ft,H=100ft.
Find:
Power generated by turbine (hp).
Sketch the EGL and HGL.
PLAN
Apply the energy equation from the upper water surface to the lower water surface.
Then apply the power equation.
SOLUTION
Energy equation
Power equation
121
7.85: PROBLEM DEFINITION
Situation:
Water discharges from a reservoir through a pipe and out a nozzle.
hL=0.025 L
D
V2
2g,D=1ft.
L= 1000 ft,Djet =6in.
z1=100ft,z2=60ft.
Find:
(a) Discharge (cfs).
(b) Draw the HGL and EGL.
Assumptions:
α=1.0.
PLAN
Apply the energy equation from the reservoir surface to the exit plane of the jet.
SOLUTION
Energy equation. Let the velocity in the 6 inch pipe be V6.Let the velocity in the
Continuity principle
123
Substituting into energy equation
Flow rate equation
124
7.86: PROBLEM DEFINITION
Situation:
Water moves between two reservoirs through a contracting pipe.
hL=0.02 L
D
V2
2g.
Dd=15cm,Ld=100m.
Lu=100m,Du=30cm.
z1=100m,z2=60m.
Find:
Discharge of water in system (m
3/s) .
PLAN
Apply energy equation from upper to lower reservoir.
SOLUTION
Energy equation
Flow rate equation
Substituting Eq. (2) and Eq. (3) into (1) and solving for Qyields:
125
7.87: PROBLEM DEFINITION
Situation:
Water is pumped from a lower reservoir to an upper one.
z1=90ft,z2=140ft.
L1=1000ft,L2= 2000 ft.
D1=8in,D2=8in.
Q=3cfs, hL=0.018 L
D
V2
2g.
Find:
(a) Power supplied to the pump (hp).
(b) Sketch the HGL and EGL.
Properties:
Water (68 ◦F), Table A.5: γ=62.4lbf/ft3.
PLAN
Apply the flow rate equation to find the velocity. Then calculate head loss. Next
apply the energy equation from water surface to water surface to find the head the
pump provides. Finally, apply the power equation.
SOLUTION
Flow rate equation
126
Energy equation
Power equation
127
7.88: PROBLEM DEFINITION
Situation:
Water flows between two reservoirs.
D=1m,L=300m.
H=16m,h=2m.
hL=0.01 L
D
V2
2g.
Find:
(a) Discharge in pipe (m
3/s).
(b) Pressure halfway between two reservoirs (kPa).
PLAN
To find the discharge, apply the energy equation from water surface Ato water surface
in B. To find the pressure at location P, apply the energy equation from water surface
Ato location P.
SOLUTION
Energy equation
Flow rate equation
128
129
Problem 7.89
Situation:
Water flows between two reservoirs.
T=100
◦F,so use γ=62.0lbf/ft3from Table A.5 in EFM10e
D=4ft,L=200ft.
H=35ft,h=10ft.
hL=0.01 L
D
V2
2g.
Find:
(a) Discharge in pipe ¡ft3/s¢.
(b) Pressure halfway between two reservoirs (psi).
PLAN
To find the discharge, apply the energy equation from water surface Ato water surface
in B. To find the pressure at location P, apply the energy equation from water surface
Ato location P.
SOLUTION
Energy equation
Flow rate equation
130
Energy equation between the water surface in Aand point P:
131
7.90: PROBLEM DEFINITION
Situation:
Two reservoirs are connected by a pipe with an abrupt expansion.
hL=0.02 L
D
V2
2g,Q=16ft
3/s.
Find:
Elevation in left reservoir.
Assumptions:
α=1.0.
PLAN
Apply the energy equation from the left reservoir to the right reservoir.
SOLUTION
Energy equation
Flow rate equation
Substituting into the energy equation
133
7.91: PROBLEM DEFINITION
Situation:
Water is pumped from a lower to an upper reservoir.
L1=100m,L2= 1000 m.
D1=1m,D2=50cm.
η=74%,Q=3m
3/s.
z1=150m,z2=250m.
Find:
(a) Pump power (MW).
(b) Sketch the HGL and EGL.
Assumptions:
α=1.0.
PLAN
Apply the energy equation from the upper reservoir surface to the lower reservoir
surface.
SOLUTION
Energy equation
Flow rate equation
134
Substituting into the energy equation
Power equation
135
7.92: PROBLEM DEFINITION
Situation:
Water flows out of a reservoir into a pipe that discharges to atmosphere.
hL=0.02 L
D
V2
2g,z1=250m.
z2=210m,zpipe =250m.
D=30cm,L=200m.
Find:
(a) Water discharge in pipe (m
3/s) .
(b) Pressure at highest point in pipe (kPa).
Assumptions:
α=1.0.
PLAN
Part a: First apply energy equation from reservoir water surface to end of pipe to
find the Vto calculate the flow rate.
Part b: Then to solve for the pressure midway along pipe, apply the energy equation
to the midpoint:
SOLUTION
Part a: Energy equation
Flow rate equation
136
Part b: Energy equation to the midpoint:
137