Question

A cylinder of height 20m is completely filled with water. Find the velocity of efflux of water (in \[m{s^{ - 1}}\]) through a small hole on the side wall or the cylinder near its bottom.
A. \[10\,m{s^{ - 1}}\]
B. \[20\,m{s^{ - 1}}\]
C. \[25.5\,m{s^{ - 1}}\]
D. \[5\,m{s^{ - 1}}\]

Answer 1

Hint:Before going to solve this question let us understand Bernoulli's principle. Bernoulli's principle states that when an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy.

Formula Used:
Using Bernoulli’s principle we have,
\[v = \sqrt {2gh} \]
Where, h is height and g is acceleration due to gravity.

Complete step by step solution:
Consider a cylinder its height is 20 cm and is completely filled. In this situation suppose a hole is made at the bottom. We need to find the velocity of water that is coming out from the cylinder. Using Bernoulli’s principle we can write as,
\[v = \sqrt {2gh} \]
Here, they have given the height, \[h = 20\,cm\] and \[g = 10\,m{s^{ - 2}}\]

Substitute the value in the above equation we get,
\[v = \sqrt {2 \times 10 \times 20} \]
\[\Rightarrow v = \sqrt {400} \]
\[\therefore v = 20\,m{s^{ - 1}}\]
Therefore, the velocity of efflux of water through a small hole on the side wall or the cylinder near its bottom is \[20\,m{s^{ - 1}}\].

Hence, option B is the correct answer.

Additional information:The Archimedes principle states that when an object is immersed in a fluid, it experiences some buoyant force that is equal in magnitude to the force of gravity on the displaced fluid. It is also referred to as the law of buoyancy. The weight of the displaced fluid is equal to the subtraction of the weight of an object in a vacuum and the weight of an object in a fluid.

Note: Here, it is important to remember Bernoulli's principle which relates the pressure of a fluid to its elevation and its speed. This equation is used to approximate these parameters in water, air, or any fluid that has a very low viscosity.