What Is the Minimum Pipe Diameter for Oil Transport in Horizontal Flow?

[ld080]

Homework Statement

Oil must be transported over a distance L through a horizontal pipe at volume flow rate of Q, using a pump with power W. Find the minimum pipe diameter, D, which guarantees the exit pressure of Pe.Common values:

sigma=(pipe roughness) = 0.05 mm
pi=(pressure at the inlet of the pump) = 10 kPa gauge,
rho=(kinematic viscosity) = 4 X 10-6 m2/s
gamma=(specific weight) = 7 kN/m3
L =
Q =
W =
Pe

Homework Equations

Colebrook Equation

The Attempt at a Solution

W=will dictate what pump outlet pressure you can have for specified Q. L will dictate how developed the flow will be among other things, and the Overall D along with Q and viscosity will dictate the Re Number. You are able to adjust D, so for a specified Q would could have a Laminar, transient , or turbulent flow. I am assuming that since he what's us to use friction factor calculations for turbulent flow you will have to choose a Q and D that result in a Turbulent flow not laminar.

I've got an idea of where to go with this, but I am a bit stuck at the moment. Thank you for any help I may get..

 

[KataKoniK]

Thank you for your post. I am a scientist with expertise in fluid mechanics and I would be happy to assist you with this problem.

To find the minimum pipe diameter, D, we can use the Colebrook equation, which relates the friction factor, pipe roughness, Reynolds number, and other variables to calculate the pressure drop in a pipe. We can rearrange this equation to solve for D as follows:

D = 4 * Q * sqrt(f) / (pi * rho * L * sqrt(2 * g * Pe))

Where:

Q = volume flow rate
f = friction factor
pi = pressure at the inlet of the pump
rho = kinematic viscosity
L = distance of pipe
g = acceleration due to gravity
Pe = exit pressure

To solve for the friction factor, we can use the Moody chart or the Swamee-Jain equation. Once we have the friction factor, we can plug it into the equation above to solve for the minimum pipe diameter.

However, it is important to note that the minimum pipe diameter will also depend on the required velocity of the oil flow, which is determined by the specific application. So, it is important to consider the velocity requirements in addition to the pressure drop calculations.

I hope this helps. If you have any further questions or need clarification, please don't hesitate to ask. Good luck with your calculations!