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.

Introduction to Break Pressure Tank (BPT)

This Article will help to understand the basics of Break pressure tank. which will help you to find the list out various types of break pressure tank and its design.

In short it is known as BPT. It is use to provided in the long pipelines. Its function is to break the pressure in the pipeline. Generally it is use to avoid the negative pressure in the pipeline by placing at the peak level in the pipeline. 

It seems like Tank or Reservoir, but its function is totally different. Therefore it should not designed for storage of water. Guidelines for sizing of BPT is available but no such software covers it as per my knowledge. Therefore it is tough to design following guidelines and solving differential equations. This blog will suggest you the dimension of BPT after solving governing equations. Before going through governing equation, I would like to discuss the types of BPT.

Types of BPT

1. Average slope of pipeline is greater than the slope of  energy gradient line (Pipe line having decreasing slope)
   
   

   
   
   

   
   

   
   In other word hydraulic gradient line will below the average slop of pipeline. which means that frictional losses will always less than static height (Bottom level of BPT - Top water level of Delivery reservoir) at full flow condition. In addition to above pipeline alignment will be such that no water will remains in the pipe line at no flow condition. Average slope of pipeline is less than the slope of  energy gradient line 
2. Average slope of pipeline is less than the slope of  energy gradient line (Pipe line having decreasing slope)
   
   In other word hydraulic gradient line will above the average slop of pipeline. which means that frictional losses will more than static height (Bottom level of BPT - Top water level of Delivery reservoir) at full flow condition. But pipeline alignment will be similar to the 1st one i.e. no water will remains in the pipe line at no flow condition.
   
   
3. Average slope of pipeline is less than the slope of  energy gradient line, but (Pipe line having decreasing slope and then increasing (Like inverted siphon)
    
   
   

Hydraulic gradient line will below the average slop of pipeline like Type -2. But water will remains in the pipe line at no flow condition as shown in above figure.

From above types  following points can be observe.

1.  Size of type -1 < Size of Type -2 < size of type -3
2.  Height of type -1 & Type -2 BPT can be finalized from Static Hydraulic Gradient line. Height of BPT may consider with 1 to 2 m margin over HGL.
3. Area of type -1 and type-2 may be 2 to 3 times of the pipelines. 
4. No need to solve any equation for finalizing the size of type-1 & type-2  BPT 
5. Type -3 BPT needs numerical analysis to finalize the area and height.

For Modeling and Numerical analysis click here.