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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