The document discusses principles and equations for measuring flow rate using Bernoulli's equation. It covers: 1) Bernoulli's equation relates pressure, velocity, and elevation in fluid flow, and is used in many flow measurement devices. 2) Flow through sluice gates can be calculated using Bernoulli's equation, relating flow rate to gate width and height difference. 3) Weirs can also be used to measure flow rate, with the flow rate proportional to the water height above the weir raised to the 3/2 power.

1. THE BERNOULLI EQUATION
FLOW RATE MEASUREMENT
All the measurement devices use the physical principle:: an increase in velocity
result in a decrease of pressure
p1+
1
2
ρv1
2
= p2+
1
2
ρv2
2
Q=A1 v1=A2 v2
Q=A2
√ 2( p1− p2)
ρ(1−(A2 / A1))
2
Qr < Q, depending on geometry
from 2% up to 40%

2. THE BERNOULLI EQUATION
FLOW RATE MEASUREMENT
Example

3. THE BERNOULLI EQUATION
FLOW RATE MEASUREMENT
Sluice gates
p1+
1
2
ρv1
2
+γ z1= p2+
1
2
ρv2
2
+γ z2
Q=A1 v1=A2 v2
b z1 v1=b z2 v2
p1= p2=0
Q=z2 b
√2g(z1−z2)
1−(z2 / z1)
2
if z1≫z2 : Q=z2 b√2gz1

4. THE BERNOULLI EQUATION
FLOW RATE MEASUREMENT
Sluice gates
Example
Q=z2 b
√2g(z1−z2)
1−(z2 / z1)
2
Contraction coefficient:
CC aprox0.61if 0<z/a<0.2

5. THE BERNOULLI EQUATION
FLOW RATE MEASUREMENT
Weir
From free jet theory, it can be assumed that
v∼√2gH
Then
Q=C1 H b √2gH=C1 b √2g H
3/2
C1 is an unknown constant to be determined experimentally.
Q∼H
3/2
for rectangular weirs

6. THE BERNOULLI EQUATION
FLOW RATE MEASUREMENT
Weir
Example
v∼√2gH
A=H
2
tan θ
2

7. THE BERNOULLI EQUATION
FLOW RATE MEASUREMENT
Weir
Example