When three or more reservoir are connected by means of pipe having one junction is called as branched pipe.

Let three reservoir are A, B and C are connected at junction D.



From shows, the flow from reservoir takes place to junction D. The flow from B takes place to junction D and the flow from Junction D is towards reservoir C.

Consider flow from A to D, applying Bernoulli’s equation.

Z_A = Z_D + P_D/ γ + hf₁

For flow form B to D, applying Bernoulli’s equation,

Z_B = P_D/ γ + Z_D + hf₂

For flow from D to C, applying Bernoulli’s equation.

Z_D + P_D/ γ = Zc + hf₃

Where  hf = head loss due to friction,

h_f = fLQ² / 12.1d⁵

From continuity equation,

Discharge through AD + discharge through Bd = discharge through DC

Q₁ + Q₂ = Q₃

With the help of these four equation, the unknown value of branched pipes can be determined.

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