TIME OF EMPTYING A HEMISPHERICAL TANK THROUGH AN ORIFICE

We were discussing the basic difference between orifice and mouthpiece, classification of orifices and mouthpieces, advantages and disadvantages of orifices, hydraulic coefficients, experimental process to determine the hydraulic coefficients, flow through fully submerged orifice, flow through partially submerged orifice and also time of emptying a tank through an orifice fitted at its bottom in the subject of fluid mechanics in our recent posts.

Now we will go ahead to find out the method to determine the time of emptying a hemispherical tank through an orifice at its bottom with the help of this post.

Let us consider we have one hemispherical tank filled with a liquid up to a height of H₁. Let us consider that one orifice is fixed at the bottom of the hemispherical tank. We are interested here to determine the time taken in emptying the hemispherical tank.

Let us consider the following data from above figure.

R = Radius of the hemispherical tank

A = Area of the tank

a = Area of the orifice

H₁= Initial height of the liquid in the hemispherical tank

H₂= Final height of the liquid in the hemispherical tank

T = Time taken in emptying the tank from H₁to H₂.

Time taken in emptying the hemispherical tank from H₁to H₂ will be given by following formula as mentioned here.

Let us determine the time emptying the tank, H₂will be zero.

This is the expression for the time emptying the hemispherical tank fitted with orifice at its bottom.

Now we will go ahead to find out the method to determine the time of emptying a circular horizontal tank through an orifice at its bottom, in the subject of fluid mechanics, in our next post.

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