Finding the pressure in a pipe?

[miamirulz29]

Homework Statement

The 810 mile long alaskan pipeline has a capacity of 2.48e5 m^3/day of oil per day. Along most the pipeline the radius is 60cm. Find the pressure at a point where the pipe has a 30cm radius. Take the pressure in the section with radius 60cm to be 190kPa and the density of oil to be 800 kg/m^3. Assume laminar nonviscous flow. Answer in units kPa

Homework Equations

q= delta v/ delta t

The Attempt at a Solution

My final equation is Pi + [rho(q^2)]/2pi^2 * (1/Ri^4 * R^4).
Is that correct?

 

[CFDFEAGURU]

A quick way that you can check your equation is with the units.

Does you equation produce a unit in kPa?

Thanks
Matt

 

[kerimek]

I would first clarify the units of the given data. The capacity of the pipeline is given in cubic meters per day, while the radius is given in centimeters. Therefore, the first step would be to convert the radius to meters (1 meter = 100 centimeters). This would give us a radius of 0.6 meters for the section with radius 60cm and 0.3 meters for the section with radius 30cm.

Next, I would use the equation for pressure in a pipe, which is P = rho*g*h, where P is pressure, rho is density, g is the acceleration due to gravity, and h is the height of the column of fluid. In this case, we can assume h to be the length of the pipeline (810 miles = 1.3e6 meters). So, the pressure at the section with radius 60cm would be P = 800 kg/m^3 * 9.8 m/s^2 * 1.3e6 m = 10.24e9 N/m^2 = 10.24 GPa.

To find the pressure at the section with radius 30cm, we can use the equation P = rho*g*h * (Ri^2/R^2), where Ri is the initial radius (60cm) and R is the final radius (30cm). This would give us a pressure of P = 800 kg/m^3 * 9.8 m/s^2 * 1.3e6 m * (0.6^2/0.3^2) = 20.48e9 N/m^2 = 20.48 GPa.

Finally, we can convert the pressure to kPa by dividing by 1000, giving us a pressure of 10.24 GPa = 10.24e6 kPa for the section with radius 60cm and 20.48 GPa = 20.48e6 kPa for the section with radius 30cm. Therefore, the pressure at the point where the pipe changes from 60cm to 30cm radius is 20.48e6 kPa.