FLOW THROUGH BRANCHED PIPES

We were discussing the basics of shear stress in turbulent flow, minor head losses in pipe flow, hydraulic gradient and total energy line, basic concept and working of syphon, flow through pipes in series and also the concept of flow through pipes in parallel, in the subject of fluid mechanics, in our recent posts. 

Now we will go ahead to see the, flow through branched pipes, in the subject of fluid mechanics, with the help of this post. 

Flow through branched pipes 

Flow through branched pipes could be defined as the fluid flow through a piping system where three or more than three reservoirs will be connected with each other with the help of pipes and will have one or more than one junctions. 

Now we will see here one figure as displayed here. Three reservoirs are connected here with the help of piping system and this piping system and reservoirs are connected with one single junction i.e. junction D. 

In various branched pipe flow problems, we will have some specifications of branched piping system and usually we will have to determine the flow of fluid through each pipe. 

Let us assume that we have information about the data for length of pipes, diameter of pipes and coefficient if friction for each pipe and we need to find the data for flow of water through each pipe. 

Assumption 

Let us assumed that reservoirs are very large and levels of water surface in the reservoirs are constant in order to secure the steady conditions in the pipes. We have also assumed that minor losses are very small and could be neglected. 

Principle and equations used for solving such problems 

We will have to recall the following principles and we will have to use following equations for securing the desired data for such problems. 

• Continuity equation 
• Bernoulli’s equation 
• Darcy-Weisbach equation

Let us consider that three reservoirs are A, B and C and piping system will have pipe 1, pipe 2 and pipe 3 and a single junction D as displayed above in figure. 

Flow of water from reservoir A will take place to junction D and flow of water from junction D will be towards reservoir C. 

Flow of water from junction D to reservoir B will only possible if piezometric head at D will be more than the piezometric head at B. 

Let us consider the following terms from above figure. 

Z_A, Z_B and Z_C = Datum head at reservoir A, B and C respectively 

V₁, V₂ and V₃= Velocity of flow of water through pipe 1, 2 and 3 respectively 

L₁, L₂ and L₃ = length of pipe 1, 2 and 3 respectively 

h_f1, h_f2 and h_f3 = loss of head for pipe 1, 2 and 3 respectively 

Let us now use the concept of Bernoulli’s equation for flow from A to D and we will have following equation as mentioned here. 

Let us now use the concept of Bernoulli’s equation for flow from D to B and we will have following equation as mentioned here.

Let us now use the concept of Bernoulli’s equation for flow from D to C and we will have following equation as mentioned here.

Now we will use the concept of continuity equation and we will have following equation as mentioned here. 

Discharge through AD = Discharge through DB + Discharge through DC 

Now as we can see that we are having with above four equations and we have to secure the value of V₁, V₂ and V₃. 

We will use above four equations to secure the value of flow of water through each pipe. 

Further we will go ahead to find out the basic concept of power transmission through pipes, in the subject of fluid mechanics, with the help of our next post. 

Do you have any suggestions? Please write in comment box. 

Reference:   

Fluid mechanics, By R. K. Bansal   

Image courtesy: Google  

Also read  

Clausius theorem 

Carnot cycle and its efficiency 

Boyle’s law 

Charles law 

Thermodynamic state, path, process and cycles 

Pure substance in thermodynamics 

Steady flow process in thermodynamics