Question

5.

(a) Write down the Bernoulli’s equation and the continuity equation.

(b) The entry and exit mouths of an uneven water pipe have areas of 0.2 m2 and 0.05 m2, respectively. If water enters the pipe at a speed of 5m/s find the speed of water exiting the pipe.

Answer 1

a) Bernoulli's equationsays that sum of total energy per unit volume ( Pressure + Kinetic + potential ) is constant for an ideal fluid. i.e.

where P is pressure, is density and h is height of fluid.

Principle of continuity is the law of conservation of mass in fluid dynamics. It states that when an ideal (Incompressible and non viscous ) liquid flows in a streamed line motion through tube of non uniform cross section, then its mass flow rate is same ,everywhere in the tube. i.e.

  

b) Given : Area at entry point i.e. A1= 0.2 m2

   Speed of water at enery point i.e V1 = 5 m/s

   Area at exit point i.e. A2 = 0.05 m2

We have to find speed of water at exit point.

Equation of continuity is is written as

putting the above value in this equation, and using    , we get :

  

   By solving this, we get

Hence speed of water at exit point will be 20m/s