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The application of Appropriate Technology

# Part 6. Imperfect Systems – Friction and the Bernoulli Equation

Of course in the real world, systems are not perfect. Energy is lost from a real system as friction. This is the sound and heat generated by the fluid as it flows through the pipes. These forms of energy are lost by the fluid rubbing against the walls of the pipe, rubbing against itself and by turbulence in the flow. The amount of frictional loss is affected by the following parameters:

1. The length of the pipe. The longer the pipes the greater the frictional losses.
2. The roughness of the pipe walls. The smoother the surface of the pipe the smaller the frictional losses.
3. The diameter of the pipe. The smaller the diameter of the pipe the greater the frictional losses.
4. The velocity of the fluid. The greater the velocity of the fluid the greater the frictional losses.
5. The type of flow of the fluid. Turbulent flow creates greater friction losses than laminar flow.
6. Changes in the shape or section of the pipe. Fittings, valves, bends etc. all increase frictional losses.

Frictional losses are non-linear. This means that if you double one of the above parameters then the frictional losses can triple or quadruple in size. Also if there is no flow there are no frictional losses. Appendix 3 gives a fuller explanation of the relationship between the above variables.

Friction is included as a term in the Bernoulli Equation (usually on the right hand side) because it represents a fraction of the overall total energy at a point in the system, although it has been lost in between those two points. Equation (13) is the Bernoulli Equation including the friction term as a pressure (fp).

$P_1 + \frac{1}{2}.\rho .v_1^2 + \rho.g.h_1 = P_2 + \frac{1}{2}.\rho .v_2^2 + \rho.g.h_2 + f_p$

(13)

In practice frictional head loss (fh) is calculated from tables that require pipe type, diameter, length and flow rate. Frictional head loss can be converted into frictional loss as a pressure by the following relation:

$f_p = f_h.\rho.g$

(14)

So Equation (13) can be rewritten as:

$P_1 + \frac{1}{2}.\rho.v_1^2 + \rho.g.h_1 = P_2 + \frac{1}{2}.\rho.v_2^2 + \rho.g.h_2 + f_h.\rho.g$

(15)