Fluid mechanics ProblemWatch this thread
A pipeline connects 2 reservoirs. The difference in water level between the reservoirs is 10 m. The pipeline consists of an upstream section of length 1500 m and diameter 750 mm and a downstream section of length 1000 m and diameter 500 mm. Ignoring minor losses and using the Darcy-Weisbach equation to calculate friction losses with λ= 0.0165 for both pipelines, calculate the discharge.
Do we neglect the velocity since the problem concerns reservoirs?
Any tips for starting this question off?
once you have done that use the Bernoulli loss equation which is work done = (P2-P1)/rho + 1/2(V2^2 - V1^2) + g(Z2-Z1) + gHL
where P1/P2 is pressure at point 1 and point 2 respectively, V is velocity, Z is height from a datum, HL is head loss (in this case purely frictional).
Once thats done you are right, we set the velocity of the reservoir to 0. Even those as water flows the water level will drop, this drop is so small over a large amount of time, compared to the velocity of the water in the pipe, it can be neglected. Work done is also 0 here since no work is being done on the water and neither is the water doing work on something.
In this one, i think you will have to set the velocities as just V1 and V2 for comparing pipes and stuff and for head loss since we dont actually know velocity and so that's what you are trying to work out. Say v1 is the velocity of the water in pipe 1 and v2 is the velocity of water in pipe 2, you can compare the 2 in terms of each other using continuity and then solve simultaneously to get rid of V1 or V2 which will leave you with just 1 term which you can then solve to find the discharge/volumetric flow rate.
Hope that helps!