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# Manual headloss calculation benchmark with MES software

In MiTS software, we are using Hazen-Williams Equation as shown below to calculate the head loss.

Hazen-Williams Equation:
$$V = kC\left(\frac{D}{4}\right)^{0.63}S^{0.54}$$

where;

$S = \frac{h_{f}}{L}$

$Q = \frac{V \pi D^{2}}{4}$

## MiTS Software#

1. The output value from MiTS software is shown as per image below.

1. We also test the value given in our software with an online head loss calculator.
3. Node 1 is taken as an example, please refer image below:
1. As you can see that the result generated from MiTS software is equivalent to the one calculated by the online head loss calculator.
• Velocity = 0.3883 m/s
• Head Loss = 0.2040 m

## Manual Calculation #

1. We used the formula below to calculate the head loss with known Discharge, Q ($m^3/s$), Pipe Diameter, D (m), Pipe Length, L (m), and Hazen-William Coefficient, k, of the material used.

Hazen-Williams Equation:
$$V = kC\left(\frac{D}{4}\right)^{0.63}S^{0.54}$$

where;
$S = \frac{h_{f}}{L}$

$Q = \frac{V \pi D^{2}}{4}$

2. As the Q is known, we will need to rearrange the equation to find the value of V.
$$Q = \frac{V \pi D^{2}}{4}$$
$$V = \frac{4Q}{\pi D^{2}}$$
$$V = \frac{4 \cdot \frac{3.050}{1000}}{\pi \cdot \left(\frac{100}{1000}\right)^2}$$
$$V = 0.3883\text{ m/s}$$

3. After obtaining the value for V, we will rearrange the Hazen-William Equation to get the value for S.
$$V = kC\left(\frac{D}{4}\right)^{0.63}S^{0.54}$$
$$S = \left(\frac{V}{kC\left(\frac{D}{4}\right)^{0.63}}\right)^{\frac{1}{0.54}}$$
$$S = \left(\frac{0.3883}{0.85\cdot 100\cdot \left(\frac{100\div1000}4\right)^{0.63}}\right)^{\frac{1}{0.54}}$$
$$S = 0.00343$$

4.Finally, we can calculate the value for hf.
\begin{aligned} S &= h_{\mathit f}\mathit\;\mathit/\mathit\;L \\ h_f &= S\mathit\;L \\ h_f &= 0.00343\times59.466 \\ h_f &= 0.2040\;\text{m}\end{aligned}