Introduction to type of flow in pipeline.

In water flow system, mainly two types of flow exist, transient flow and steady flow. Here I will elaborate both types. Transient flow can be study in two cases, sudden change of momentum and gradually change of momentum. Sudden change causes water hammer and it is hazardous/dangerous for the pipelines. Gradual change does not create water hammer, but it is difficult to analyse mathematically whereas Steady state flow is very simple and easy to analyse. So, let us discuss in detail.

1.    Transient flow (type – 1)

To understand the transient flow, I would like to take the following example. The following figure represents a simple water network with one source and a delivery reservoir. Let us assume that network having no flow. If there is no flow in the network, water will stagnant in the lower portion of the pipe.

Once water will enter the first reservoir, it will push the accumulated water in the forward direction. The force required to push the water is change of momentum of accumulated water plus frictional head. Let us say force “F_m” required to compensate the change of momentum, and F_f required for frictional force. This force will give the required water head to push the water. We can calculate required head  by formula.

By this head water will starts moving out to the delivery reservoir. From the following figure if can be observe that velocity at t =0 will be zero, and then it will increase gradually to attain the steady state velocity. Figure 2 is showing the situation at t=0 and figure 3 showing situation at steady state.

i.e we can write as follows

Actually ha will be the correct notation instead hm because water will be the accelerating from t =0 and then it will become zero at steady state. The above figure represents the situation at t =0 and below at steady state.

Hence, we must write like  

As we know that time is very important factor in the transition stage. If time increases in change of momentum the required force will reduce. Here is the same situation, larger area of reservoir will give more time in changing the momentum of accumulated water.  The optimum area can be calculated by following some guidelines. Many guidelines are available but no one software dealing this type of problem as per my knowledge. I request to the readers if you know any software please share with me. The guidelines available is limited to the single delivery reservoir. If you have more delivery reservoir, you must convert to the single delivery reservoir.

2.    Transient flow (type – 2)

Second type of transient flow stats with steady flow. In this flow sudden change of velocity occurs. Sudden change of velocity may have many causes like sudden close of valve, cause of column separation, single pump failure and power failure. This is also known as water hammer or surge. There are many software/applications which deals with surge like

1.      SAP (Surge Analysis Program).

2.      Water Hammer

3.      Hytran http://www.hytran.net/

4.      Kypipe http://kypipe.com/surge/

Surge is a very big chapter, and can be discuss for a semester.

3.    Steady state flow

Steady state flow is simplest flow in the pipe network. It is also known as pressure developed flow. These flows do not have change of momentum term. Its governing equation will have mass balance and energy balance equation but change of momentum will not be there.

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.