The Darcy- Weisbach Formula, Essay Example

This discussion details the Darcy- Weisbach formula in conjunction with the additional Moody diagram as the conventional method of computing energy losses which originate from the movement of fluids in a pipe. The friction of a fluid which is present between two points on a pipe may be assessed by the empirical addition to the Bernoulli equation. The formula is detailed as:

h₁ = [V²/ 2g + p¹/?g + z₁] – [V²₂/ 2g + p₂ / ?g + z₁] ? [p¹/?g + Z₁ – p₂/ ?g + Z₁]

This formula derives the frictional coefficient which may have caused the distinction from the laminar effluence to this theory. It can also be detailed as the head loss. The mean velocity is depicted by V₁ and V₂ and g is the aspect of gravitational acceleration. The density of the fluid is represented by ? and the pressure of the fluid is represented by p. The height of the pipe is represented by z.

In the circumstance of the review being limited to the area of the uniform flow, the velocity terms negate each other and the RHS is applied. The pressures in any given pipe must be assessed in order to calculate the losses. This infers that the systems must be constructed in order to observe the manner by which it will behave.

The design and engineering aspects of pipes require that a correlation be present which forecasts h₁ as an operation of the fluid, the category of the pipe and the diameter of the pipe. The formula which has been proposed by Weisbach and is currently applied is the following:

h₁ = fLV²/ D2g

This is considering that the pipe length is L. the pipe diameters is D and the friction factor is f. In this model the friction occurs in the pipe wall. The version of the formula which is applied today does not consider the aspect of the energy losses which take at the fittings, elbows and the influence of fluid viscosity. The co relational formula which considers the aspect of friction is:

f = ? + ?/ (V)^1/2

This holds true in the circumstance where the frictional coefficients are demonstrated by ? + ?. In Darcy’s analysis a non defined badly behaved section of the pipe is the critical zone. The most commonly accepted range for the laminar effluence is Re< 2000 and the flows which are turbulent take place in the range of Re> 4000.

Conclusion

The aspect of the pipe friction could have been caused by the difference in the pipe substance and the pipe diameter. An additional source of the difference in the real and the laboratory values could be attributed to the friction which took place inside of the pipe.

References

Brown, G. (n.d.). The history of the Darcy- Weisbach equations for pipe flow resistance. Oklahoma State University.