When solving many fluid dynamics problems, be it steady state or transient, the Darcy-Weisbach friction factor, f, is necessary. In circular pipes this factor can be solved directly with the Swamee-Jain equation, as well as others, however most of these equations are complicated, and become cumbersome when iteration is necessary. Therefore, it is often effective to solve for this friction factor using the Moody Chart.
- As with many fluid mechanics problems, the first order of business is to determine the Reynolds number of the flow. If you don't have a velocity by which to calculate the Reynolds Number, you will need to assume either a velocity, or a initial friction factor. If you assume an initial velocity, proceed as usual. If you assume a friction factor (I like 0.02), jump to step 10. If done correctly, you will converge at the same answer.
- Refer to the Moody Chart. If the Reynolds Number falls in the Laminar or Transition range, refer to appropriate equations. If however the flow is in the Turbulent range, we are ready to proceed with the Moody Chart.
- Compute the relative pipe roughness. This value is the roughness of the pipe, divided by the diameter of the pipe. REMEMBER, you want this to be unitless, so ensure that the roughness and diameter are in matching units.
- ALSO REMEMBER, just because the wall roughness may be zero, making the relative roughness zero, this does NOT mean that the friction factor will be zero.
- Find the line referring to your relative roughness on the right side of the diagram. In the case that your value does not have a printed line, imagine a line paralleling the nearest line representing your relative roughness. It may be helpful to sketch in this line.
- Follow this line to the left as it curves up until to reach the vertical line corresponding to your flow's Reynolds Number.
- Mark this point on the Chart.
- Using a straight edge, follow the point straight left, parallel to the x axis, until you reach the far left side of the chart.
- Read off the corresponding friction factor.
- Calculate the energy losses knowing the friction factor.
- Calculate a new velocity and Reynolds Number.
- Compare your new Reynolds Number with your previous value. If the Reynolds number is appreciably different from your previous value, repeat the calculations with this new Reynolds Value. If however it is close to your previous value, your answer has converged, and you are finished.
Let's imagine we calculate a Reynolds Number of 4x10^4 (yes I'm rigging for simplicity). We see that this is in the Reynolds Number range for turbulent flow, so we proceed with the Moody Chart. Next, let's say we calculate a unitless relative roughness of 0.003. From here we sketch a line following the curve contours, going left, as see in the red line below. We follow this line until you Reynolds number value from before, and mark this point. From here, we look straight left, shown by the orange line, until we hit the left margin of the chart. Here we read off our value of 0.03.
At this point, we would compute a new velocity, and a new Reynolds Number, and iterate if necessary.
Other things to be aware of
- Both the Reynolds number and relative roughness are unitless values when computed correctly, therefore the Moody Chart is unitless, so the same chart applies to US Customary and SI unit systems.
- Another common mistake when reading the Moody Diagram is improper interpolation between lines and points. Be aware of the logarithmic nature of the axes and labels values, halfway between the values is NOT halfway between the points
- This system will only work for steady state analysis. If the problem is transient, you can still solve for the end state, however no information can be gleaned from what happens between initial state and steady state. To do this, other methods including numerical analysis, or FEA will be necessary.
Raj Kc on July 19, 2017:
For the new velocity we have to use the net head??
like new assume velocity = (2*g*Hn)^0.5
where Hg= Gross head
Hl = Head loss
Patrick on December 29, 2016:
I wish that all these adds were not littering and obstructing your page.