How Do You Calculate Fluid Velocities in Diverging Pipes?

[andz]

Homework Statement

Flow in a pipe splits into two parallel pipes. All three pipes have same length L, and same friction factor f. Diameter of first pipe is D. The two parallel pipes have diameter D and D/2. All three pipes are on same horizontal level. At the outlet of the two parallel pipes, the pressure is equal to atmospheric pressure. Minor losses can be neglected. The density of the fluid is constant. In this situation we can use this information: D = 0.03 meters, f = 0.02, L = 8 meters, pressure head at inlet of first pipe = 2 meters, g = 9.8 m/s^2.

I need to find the velocities in all three pipes.

Homework Equations

Continuity equation.
Bernoulli equation.
Darcy-Weisbach equation

The Attempt at a Solution

Due to conservation of mass, the continuity equation gives: Q1 = Q2 + Q3. This gives 1) A1V1 = A2V2 + A3V3.
Then I tried to apply bernoulli equation from inlet of the first pipe to outlet of both parallel pipes.
2) H1 - hf = H2 (H1 = total head at inlet of first pipe, hf = friction loss in pipe).
3) H1 - hf = H3

2) 2 + (V1^2)/2g - (fLV1^2)/2gD - (fLV2^2)/2gD) = (V2^2)/2g
3) 2 + (V1^2)/2g - (fLV1^2)/2gD - (fLV3^2)/2gD) = (V3^2)/2g
Is this correct so far and how do i solve this?

 

[BvU]

Hello Andz,

Looks good to me so far. You have 3 equations with three unknowns. Be careful not to use D for two different diameters.
I would rewrite 2) - 3) to eliminate v₃² and express it in v₂².