Governing Equation of Break Pressure Tank (BPT)

As we have discussed Basics of BPT and its various type. We can proceed for governing equations and numerical analysis.

From the below figure it is clear that water will stagnant in the inverted siphon portion (from point C to D) in no flow condition.  As the steady state flow Qo enters to the BPT, filling of the liquid will start from upper portion of the inverted siphon (from point C to towards BPT). This coming water will create head difference to push the stagnant water to move towards the delivery reservoir. As the water starts filling, it will continue up to the BPT to attain steady state condition. Now this situation can be described by Continuity Equation and conservation of Momentum equation in the following cases.

Case –1: Filling starts from upper portion of the inverted siphon.

1.        Continuity Equation (Conservation of Mass)

Putting the value or l = h cosec θ in above equation.

2.       Conservation of momentum.

Change of momentum of stagnant liquid = Force applied in the liquid due to static head of fluid.

Or,  Change of momentum of fluid = Static Head – Frictional Head.

Writing the terms

Case –2: Filling starts from Bottom of the BPT.

3.       Continuity Equation (Conservation of Mass)

4.       Conservation of momentum.

In usual practice pipe line does not leave to drain out. Because once pipe got empty, its takes time to refill the pipeline and required demand will not deliver to the delivery reservoir. This happens, when pipeline inclination θ is very less and pipeline length is long. Therefore delivery valve turned off in such a way that next time filling starts from bottom of the BPT.