M E 320 Professor John M. Cimbala Lecture 14
Today, we will:
•
Do another example problem – head form of the energy equation
•
Discuss grade lines – energy grade line and hydraulic grade line
•
Derive and discuss the Bernoulli equation
5. Examples (continued)
Example – Water draining from a tank
Given: Water drains by gravity from a tank exposed to atmospheric pressure. The vertical distance
from the pipe outlet to the surface of the water in the tank is Δz = 0.500 m. The irreversible head
losses in the piping system (due to friction in the pipe, losses through the valve, elbow, etc.) are
estimated as h
L
= 0.400 m of equivalent water column height. Note: You will learn how to calculate
the irreversible head losses associated with piping systems on your own in Chapter 8.
Open valve
V
2
Δz
To do: Calculate the average velocity at the outlet, V
2
.
Solution:
From previous lecture…use the head form of the conservation of energy equation:
22
11 2 2
1 1 pump,u 2 2 turbine, e
12
22
L
PV P V
zh zh h
gg gg
αα
ρρ
⎛⎞⎛ ⎞
+++ =+ ++ +
⎜⎟⎜ ⎟
⎝⎠⎝ ⎠
∑∑
