Young and Freedman, Example 14.7
Water enters a house through a pipe with an inside diameter of 2.0cm at an absolute pressure of 4.0x105 Pa. A
1.0-cm-diameter pipe leads to the second floor bathroom 5.0m above. When the flow speed at the inlet pipe is
1.5m/s, find the flow speed, pressure, and volume flow rate in the bathroom.
Given: D1=2.0cm
D2=1.0cm
P1=4x105 Pa
v1=1.5 m/s
h1=0 (datum at inlet)
h2=5.0 m (datum at inlet)
ρwater = 1000 kg/m3
second floor
(1-cm pipe) 2
5m
Required: flow speed in bathroom, v2
Pressure in bathroom, P2
volume flow rate in bathroom, Q2
1
water
heater
From water supply
(2-cm pipe)
Solution: Since we have more than one unknown, we need to use both continuity and Bernoulli equations
•
Use continuity to find v2:
•
Use Bernoulli to find P2:
4
•
10 Pa
.
.
1.5
1000kg/m% &
4
10 Pa
volume flow rate: Q=vA
-
6
convert:
'
= 6.0 m/s
.
(
0.17 10 Pa
= 3.3 x 105 Pa
0.49
0 . 005m
4.7
m
s
2.3
45 +
6
7
6
1000kg/m% 9.81 +
10 Pa
1012 m% /s
= 0.47 L/s
5m
0