Unsteady Flow in Pipes

The flow in which flow parameters such as velocity, pressure and density of a fluid flow are dependent upon time is called unsteady flow.

In pipe lines when the valves are operated then the flow parameters changes with respect to time and its state becomes unsteady.

 

Transient Time

• The time required for the unsteady flow to become steady.
• Transient time is important to know so that the closing or opening times of the valves can be adjusted.
• Due to unsteadiness high and low pressure waves develop in the pipes.
• If not controlled the pipes can burst due to high pressure or collapse due to low pressure.

• For Transient Time Writing Energy Equation Between Point 1 And 2

Equation.1

• If there is atmospheric pressure at both sections 

 

• If datum is at pipe central line then

 

• The head loss is due to

1. Separation losses 
2. Pipe friction

• Unsteady flow energy balance also known as accelerative head is  given by

 

• So head loss is
  
  Equation.2

• The energy equation becomes

Equation.3

f = pipe friction factor

K = Separation Losses

• Finally Equation 1 becomes

Equation.4

• When valve is opened the head H is used to accelerate the flow at such a value at which the head is balanced by frictional and minor losses.
• The state becomes steady.
• The energy equation can be written as

Equation.5

• Comparing equations 4 and 5,

Equation.6

 Equation.7

• By integration,

Equation.8

• So the transient time is given by 

Equation.9