Question

3 reservoir problem

Reservoir A: 150m

Reservoir B : 125m

Reservoir C : 75m

The pipes from each reservoir meet at junction J. The characteristics are as follows (all in meters:

La Lb Lc. Da Db Dc

500 1000. 750.  0.75 1 1  

What are the friction factors for each pipe?

What is the correct elevation of J in meters ?

What are the flows in each pipe?

Answer 1

Assume that Reynolds number = 2000

So friction factor = 64/2000 = 0.032

So we have

Assuming that the liquid level in each reservoir is constant and the surface is open to atmosphere, the Bernoulli Equation for Reservoir i (where i=1, 2 and 3) is

But we know that Q = AV and A = pi * diameter²/4

so we get

Additionally, the sum of the flowrates from each reservoir is equal to the external demand

We need to solve this in excel, we do not know the initial flow rates, so we have to assume some head for J and find the error

Use excel solver to minimize the total error

Assuming that minor loss coefficient is zero we have the following for the three reservoirs A, B, C

So solving we get

so correct elevation of J = 112.157m

and flows in pipes A,B,C are -2.606, -1.722 and 4.328 cubic meters/sec

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