Monday, December 29, 2014

Velocity of Efflux and Venturi Meter

Velocity of Efflux

When a vessel is having a small opening above whom there is certain level of water, we can calculate the velocity of the water that is coming out of the opening using this concept. This is nothing but a direct application of  Bernoulli’s theorem.

We can apply that the total energy at the given two points is always constant.One point of consideration is that the surface of the vessel with a larger opening and other point in the consideration is having the small opening. Being the area of the larger par is  bigger the velocity with which it comes down there is negligible.

Similarly being both the parts of the system are open to atmosphere, both of them are having the same pressure which is equal to atmospheric pressure. We can prove mathematically that velocity with which the fluid comes out is equal to the velocity of a freely falling body.

Time taken to empty the tank

Basing on the above concept and using the concept of integration together we can derive the equation for the time taken to empty a vessel as shown below. Here we are using the concept of equation of continuity also.

Venturi Meter

It is a device using which we can calculate the velocity of the fluid. It has a pipe with a larger opening which keeps on decreasing and a particular point the it is having a small opening.

These two points are horizontal to each other and they are having the same potential energy at the two points. We can apply the law of  conservation of energy concept that the two points and by applying the equation of continuity together we can derive the equation for the velocity as shown below.

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