Minor Loss in Water Reticulation

Minor losses may occur at a change of section, valve, bend or other interruption. In MiTS 3, the user can specify the minor loss coefficient in the pipe. This means the user can include the minor loss in the head loss computation. Calculation of total head loss computation will include both minor and major losses that occurred in the pipe.

The formula for calculating the major head loss is:

$$Hmajor\:=\:S\:\times \:L$$

The formula for calculating the minor head loss is:

$$Hminor\:=\:k\:\times \:\frac{v^2}{2g}$$

Where,

S = Energy Slope

L = Pipe Length

k = Minor Loss Coefficient

v = Velocity

Therefore, the full formula for calculating head loss in water reticulation would be:

$$Htotal\:=\:Hmajor\:+\:Hminor$$

Example #

Project File HERE

Using pipe 1 from the example project file, the computed headloss is 0.984m. Implementing the formula used to calculate this value:

Major Loss

$$Hmajor\:=\:S\:\times \:L$$

$$Hmajor\:=\:\sqrt[0.54]{\frac{v}{kC\left(\frac{D}{4}\right)^{0.63}}}\:\times \:L,\:[k\:and\:C\:are\:Hazen-William\:coefficients\:of\:material\:used]$$

$$v = 1.382; k = 0.85; C = 100; D = 200/1000; L = 59.466$$

$$Hmajor\:=\:\sqrt[0.54]{\frac{1.382}{0.85\:\times \:100\:\times \:\left(\frac{200/1000}{4}\right)^{0.63}}}\:\times \:59.466$$

$$Hmajor = 0.95354\:m$$

Minor Loss

$$Hminor\:=\:k\:\times \:\frac{v^2}{2g},\:[k\:is\:the\:minor\:loss\:coefficient]$$

$$k = 0.3; v = 1.382; g = 9.81$$

$$Hminor\:=\:0.3\times \:\frac{1.382^2}{2\:\left(9.81\right)}$$

$$Hminor = 0.029204\:m$$

Total Headloss

$$Htotal = Hmajor + Hminor$$

$$Htotal = 0.95354 + 0.029204$$

$$Htotal = 0.982744\:m$$

Conclusion

As demonstrated by the example provided above, the minor loss represents only a small fraction when compared to the major loss. The difference between these two types of losses highlights the minor loss is relatively negligible in magnitude compared to the major loss, which is far more substantial.