Project file: Head Loss here

In MiTS software, we can choose to use either Hazen-Williams Equation or Darcy-Weisbach Equation to Chezy-Manning Equation to calculate the head loss. Users can change the head loss formula used in the analysis at Options > Project Settings > Water Ret > Design > Headloss Formula

Hazen-Williams Equation #

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

where;

$$S\:=\:\frac{h}{L}$$

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

MiTS Software #

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

Online Head Loss Calculator #

1. We also test the value given in our software with an online head loss calculator.
2. You may click here for the online head loss calculator.
3. Pipe 1 is taken as an example, please refer image below:

4. As you can see that the result generated from MiTS software is equivalent to the one calculated by the online head loss calculator.

• Velocity = 0.3874 m/s
• Head Loss = 0.2031 m

Manual Calculation #

1. We used formula below to calculate the head loss with known Discharge, Q (m³/s), Pipe Diameter, D (m), Pipe Length, L (m) and Hazen-William Coefficient, k of the material used.

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

where;

$$S\:=\:\frac{h}{L}$$

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

2. As the Q is known, we will need to rearrange the equation to find the value of V.

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

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

$$V\:=\:\frac{4\left(\frac{3.043}{1000}\right)}{\pi \left(\frac{100}{1000}\right)^2}$$

$$V\:=\:0.3874\:m/s$$

3. After obtaining the value for V, we will rearrange the Hazen-William Equation to get the value for S.

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

$$S\:=\:\sqrt[0.54]{\frac{V}{kC\left(\frac{D}{4}\right)^{0.63}}}$$

$$S\:=\:\sqrt[0.54]{\frac{0.3874}{0.85\times 100\left(\frac{100/1000}{4}\right)^{0.63}}}$$

$$S\:=\:0.00342$$

4. Finally, we can calculate the value for h.

$$S\:=\:\frac{h}{L}$$

$$h\:=\:SL$$

$$h\:=\:0.00342\times 59.466$$

$$h\:=\:0.2034\:m$$

Darcy-Weisbach Equation #

$$H\:=\:\frac{fLV^2}{2dg}$$

$$f\:=\:\frac{1.325}{\left[ln\left(\frac{e}{3.7D}+\frac{5.74}{Re^{0.9}}\right)\right]^2}$$

$$Re\:=\:\frac{VD}{v}$$

where;

H = head loss

f = Darcy friction factor (Moody friction factor)

L = pipe length

V = velocity

D = pipe diameter

g = gravitational acceleration (9.806 m/s²)

e = surface roughness

Re = Reynolds Number

v = kinematic viscosity (water at 20^oC = 1.003E-6)

MiTS Software #

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

Online Head Loss Calculator #

1. We also test the value given in our software with an online head loss calculator.
2. You may click here for the online head loss calculator.
3. Pipe 1 is taken as an example, please refer image below:

4. Moody Friction Factor can be calculated using the online calculator here. Please refer image below:

5. As you can see the result generated from MiTS software is equivalent to the one calculated by the online head loss calculator:
   • Velocity = 0.3874 m/s
   • Head loss = 0.1202 m

Manual Calculation #

1. Formula below is used to calculate the head loss with known length, L (m), velocity, V (m/s), pipe diameter, D (m), pipe roughness, e (mm) and kinematic viscosity, v (m²/s)

$$H\:=\:\frac{fLV^2}{2dg}$$

$$f\:=\:\frac{1.325}{\left[ln\left(\frac{e}{3.7D}+\frac{5.74}{Re^{0.9}}\right)\right]^2}$$

$$Re\:=\:\frac{VD}{v}$$

2. Darcy friction factor is needed to calculate the head loss and Reynolds Number is needed to calculate Darcy friction factor. So we will find the Reynolds Number first.

$$Re\:=\:\frac{VD}{v}$$

$$Re\:=\:\frac{0.387\times 0.1}{1.003\times 10^{-6}}$$

$$Re\:=\:38268.793$$

3. Next, we need to find Darcy friction factor.

$$f\:=\:\frac{1.325}{\left[ln\left(\frac{e}{3.7D}+\frac{5.74}{Re^{0.9}}\right)\right]^2}$$

$$f\:=\:\frac{1.325}{\left[ln\left(\frac{0.15}{3.7\times 100}+\frac{5.74}{38268.793^{0.9}}\right)\right]^2}$$

$$f\:=\:0.26384364\:≈\:0.264$$

4. Finally, we can calculate the head loss using Darcy-Weisbach formula.

$$H\:=\:\frac{fLV^2}{2dg}$$

$$H\:=\:\frac{0.264\times 59.466\times 0.387^{2}}{2\times 0.1\times 9.806}$$

$$H\:=\:1.1989\:≈\:1.20\:m$$

Chezy-Manning Equation #

$$H=\frac{10.293\cdot \:n^2\cdot \:L\cdot \:Q^2}{d^{5.33}}$$

Notes:

H = headloss (m)

n = Manning’s roughness coefficient

L = pipe length (m)

Q = flow rate (m³/s)

d = pipe diameter

MiTS Software #

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

Online Head Loss Calculator #

1. We also test the value given in our software with an online head loss calculator.

2. You may click here for the online head loss calculator.

3. Pipe 1 is taken as an example, please refer image below:

4. As you can see the result generated from MiTS software is equivalent to the one calculated by the online head loss calculator:
   • Velocity = 0.3874 m/s
   • Friction loss (Head loss) = 0.3126 m

Manual Calculation #

Pipe 1 is used for the calculation example.

1. The following formula is used to calculate the head loss with the known value of pipe length (L), flow rate (Q), pipe diameter (d) and Manning’s roughness coefficient (n).

$$H=\frac{10.293\cdot \:n^2\cdot \:L\cdot \:Q^2}{d^{5.33}}$$

2. The known value for each parameter is as below:

$$L=59.466\:m$$

$$Q=3.043\:l/s=0.003043\:m^3/s$$

$$d=0.1\:m$$

$$n=0.016$$

3. Now, just input the value into the formula.

$$H=\frac{10.293\cdot \:n^2\cdot \:L\cdot \:Q^2}{d^{5.33}}$$

$$H=\frac{10.293\times 0.016^2\times 59.466\times 0.003043^2}{0.1^{5.33}}$$

$$H=0.3102\:m$$