Question

Applications of Bernoulli’s theorem can be seen in:

1. Dynamic lift of aeroplane
2. Hydraulic press
3. Helicopter
4. None of these

Answer 1

For the streamline flow of an ideal fluid (non viscous and incompressible),the sum of the pressure energy, kinetic energy and potential energy per unit mass is always constant.
Mathematically, we state Bernoulli’s theorem $d\dfrac{P}{\rho } + \dfrac{1}{2}{v^2} + gh =$ constant:
Whatever is true for unit mass must be true for any mass of the fluid .So, the total energy of an ideal fluid in steady flow remains constant.

Complete step by step solution:
Let’s check each of the options given in the question to find whether the option or options contain application of Bernoulli Theorem.

1)Dynamic lift of aeroplane: according to Bernoulli’s theorem , if the velocity is more ,pressure would be less and vice-versa. So, the air pressure on the upper surface of the aeroplane will be less than the atmospheric pressure. The air pressure on the lower surface will be more than the atmospheric pressure .The pressure difference produces a thrust R on the aeroplane. Thrust R is responsible for the lift of the aeroplane .

Hydraulic press: it is an application of Pascal’s law. Which states that: The pressure in a fluid in equilibrium is the same everywhere if the effect of gravity can be neglected.

Helicopter:it also uses Bernoulli’s principle for lift .

So, from the above explanation we have option 1 and 3 are correct.

Note:
Apart from such huge applications , Bernoulli’s theorem has some limitations also;
-When fluid moves in along a curved path ,energy corresponding to centrifugal force also comes into light.
-When fluid is in motion , it experiences viscous drag .This quantity has not been taken into account.
-No loss of energy was considered into Bernoulli principle ,practically it is not possible.