# Turbulent Profiles Much Flatter Laminar Profile Flatness Increases Reynolds Number Asked S Q12723189

The turbulent profiles are much flatter than the laminar profileand this flatness increases with Reynolds number. What are youasked to solve for: Volumetric flow rate can be generallycalculated using the following equation: The velocity magnitude isa function of distance from the centerline of the pipe, r. It meansthat the velocity profile is not a uniform profile but curved.However, since at every single value of r, the velocity can beconsidered constant/uniform over a ring with a thickness equal to avery small value, say dr, the flow rate equation, Q=Av, can beapplied for these rings: Based on this information, you are askedto calculate the total flow rate, Q, across the pipe cross section,for any give values of R, Vmax, and n. Write a script that takesthe following inputs.

What are you asked to solve for:

Volumetric flow rate can be generally calculated using thefollowing equation:

Q = A*V

Q: volumetric flow rate (meter^3/sec)

A: Cross section area to which flow direction is perpendicular(meter^2)

V: Velocity of the flow (meter/sec)

The velocity magnitude is a function of distance from thecenterline of the pipe, *r*. It means that the velocityprofile is not a uniform profile but curved.

However, since at every single value of *r*, the velocitycan be considered constant/uniform over a ring with a thicknessequal to a very small value, say *dr*, the flow rateequation, Q=Av, can be applied for these rings:

q= dAxv

Vr: velocity of the flow at a distance r from the centerline

dA: the area of the ring surface 2(pi)dr

Based on this information, you are asked to calculate the totalflow rate, *Q*, across the pipe cross section, for any givevalues of *R, Vmax,* and *n*.

Write a script that takes the following inputs.

Inputs to your script:

*n*

*R*

*Vmax*

Output:

– The volumetric flow rate.

– Average velocity across the cross section:

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