Question

Develop the formula for friction factor ‘f’. Keeping in mind the Re# should always be in turbulent region. What value of D should be selected to get turbulent flow. Start the value from 0.01m try to find the value of D to have the turbulent flow. Use Excel Solver tool and demonstrate how it can be used to calculate friction factor ‘f’ for a given Re# and relative roughness ?. The friction factor is desired for water flowing at 0.063 m3 /s through a cast iron pipe with a diameter of 2.75m. Using Colebrook Formula calculate friction factor. And compare it with f being taken from Moody Diagram in your text book “Fluid Mechanics by Munson”

Answer 1

The pipe flow area is

Pipe flow velocity is

We assume the fluid is water at 20⁰C

The kinematic viscosity is

The Reynold's number is

The Colebrook-White equation is as follows:

= 0.00026 m for cast iron

Using Excel equation solver, the calculated friction factor is

f= 0.0239

The formulae and set-up is given below:

Comparison with Moody diagram

With

and Re=29025

From Moody diagram

f=0.0236

Hence it agrees well with Colebrook equation.

The critical Reynold's number is

Re=2320

Hence the friction factor with Re=2320 is

The formula for Reynold's number is

If Re=2320 (for turbulent flow)

D=79895/2320=34.43 m

The friction factor with Re just greater than 2320 is(using the Excel solver again)

f=0.04716