How to Solve Fluid Mechanics Problems Using Moody Diagram

Hello my fellow science lovers and Mechanical Engineers. Today I am gonna solve an example problem of Fluid Mechanics or Fluid Power (Fluidics) using Very Important Moody Diagram. Before you start to look at the problem you can have a look at the following post - 

Problem Solving Using Moody Diagram 

Problem -   A Hydraulic oil has the kinematic viscosity of 50 cS . The oil flows through a commercial steel pipe of 1 inch diameter. Find the friction factor for the following conditions -

a. Velocity of the flow - 10 ft/s 
b. Velocity of the flow - 40 ft/s 


At first we have to find Raynolds Number from this formula, (This formula is optimized for kinematic viscosity in cS = Centistokes)


Raynolds number and moody diagram

Raynolds number for kinematic viscosity

Putting the values of all the parameters we get - 

a . Raynolds Number is 1548. So the flow is laminer (Raynolds number < 2000 )
 So here we don't need the relative roughness and hence we don't need the Moody Chart. Simply we will use the formula  for friction factor, f 

friction factor laminar flow

By using this formula we get friction factor , f = 0.042 (ans)

b. Raynolds Number is 6192 . So the flow is Turbulent (Raynolds Number > 4000)  

Now for turbulent flow we will have to use moody diagram for getting the friction factor. For that reason we have to calculate the relative roughness. Here is the equation for relative roughness.

relative roughness equation

For getting the value of epsilon we will use this chart -

typical values of actual roughness for different materials

From the chart we see that-  for commercial steel actual roughness epsilon = 0.0018 

So Relative roughness = 0.0018 in / 1 in = 0.0018 

Now get  in to the moody chart 

Locate Raynolds Number = 6192 in the Raynolds Number axis in the chart. And now go up vertically to get the value of relative roughness = 0.0018 . Now project horizontally for getting the value of f . Which is f = 0.036 (ans) . For your assistance the necessary points are shown in the diagram.

Problem solving using Moody Diagram

Thank you. If you have any question about the problem or the Moody Diagram then contact me or just leave a comment. Cheers ! Hope this will be helpful .


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