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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