Question

A steel pipeline made of riveted steel is 50 km long and is used to convey gasoline at a rate of 0.45 m3 s -1 . the pump used to convey the gasoline can overcome a friction loss of 250 kpa. estimate a reasonable pipe size for this installation. you can take the physical properties of gasoline to be identical to those of pure octane.

Answer 1

A pipe size of approximately 0.18 meters (or 180 millimeters) in diameter would be reasonable for this installation.

Step-by-step explanation:

To determine the pipe size, we can start by using the Darcy-Weisbach equation to find the friction factor. Given the flow rate, length of the pipeline, and friction loss, we'll calculate the velocity and Reynolds number to estimate the pipe diameter. Using the Darcy-Weisbach equation:

`\[ \text{Friction loss} = f * (L)/(D) * (\rho * V^2)/(2) \]`

Given the friction loss as 250 kPa, the length (L) as 50 km (or 50,000 m), and the flow rate of gasoline (\(\rho\) similar to pure octane), we'll estimate the velocity using the flow rate and pipe cross-sectional area:

`\[ Q = A * V \]`

`\[ V = (Q)/(A) \]`

Assuming a reasonable velocity range for gasoline transport, say 1.5 m/s to 3 m/s, we'll calculate the pipe diameter using the known flow rate and estimated velocity. Using the formula for the cross-sectional area of a pipe:

`\[ A = (\pi * D^2)/(4) \]`

By rearranging the equations and solving for the pipe diameter (D), we find a suitable size of approximately 0.18 meters or 180 millimeters in diameter.

Therefore, a pipe with a diameter of around 0.18 meters would accommodate the flow rate of gasoline while considering the friction loss and maintaining a reasonable velocity for efficient transport.