Head Loss Calculations - Memphis
Civil Engineering Hydraulics Mechanics of Fluids
Head Loss Calculations
Bernoulli and Pipe Flow
? The Bernoulli equation that we worked with was a bit simplistic in the way it looked at a fluid system
? All real systems that are in motion suffer from some type of loss due to friction
? It takes something to move over a rough surface
2
Pipe Flow
1
Bernoulli and Pipe Flow
? Consider flow in a constant-diameter pipe
3
Pipe Flow
Bernoulli and Pipe Flow
? If we look at the energy at points 1 and 2.
p1
+
v12 2
+ z1g
=
p2
+
v
2 2
2
+ z2g
4
Pipe Flow
2
Bernoulli and Pipe Flow
? Since this system is horizontal, z1 = z2 so
p1
+
v12 2
=
p2
+ v22 2
5
Pipe Flow
Bernoulli and Pipe Flow
? The pipe has a constant diameter and the flow is constant at both sections so the velocity at each point is the same.
v1 = v2
p1
+
v12 2
=
p2
+ v22 2
6
Pipe Flow
p1
=
p2
3
Bernoulli and Pipe Flow
? Since we are dealing with an uncompressible fluid, the pressures at points 1 and 2 should be the same.
p1
=
p2
p1 =
p2
7
Pipe Flow
Bernoulli and Pipe Flow
? If we ran the system experimentally and measured the two pressures, they would not be the same.
p1
=
p2
p1 =
p2
8
Pipe Flow
4
Bernoulli and Pipe Flow
? The pressure at point 2 would be lower than the pressure at point 1.
p1
=
p2
p1 =
p2
9
Pipe Flow
Bernoulli and Pipe Flow
? The pressure is being lost (actually the pressure energy) due to friction as the flow moves along the pipe.
p1
=
p2
p1 =
p2
10
Pipe Flow
5
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