Question

Bernoulli’s theorem is a consequence of the law of conservation of:
A. Angular momentum
B. Mass
C. Energy
D. Momentum

Answer 1

Bernoulli’s theorem states that when the speed of a fluid increases simultaneously the static pressure decreases or there is a decrease in the potential energy of the fluid and vice-versa. It is applicable to the fluid in an ideal state. Bernoulli’s equation can be used to find the quantity which is conserved. Then, we can say, Bernoulli’s theorem is a consequence of the law of conservation of that quantity.

Complete step by step answer:
Bernoulli’s equation gives the relation between the pressure, kinetic energy, and the gravitational potential energy of the fluid in a container. The fluid can be a liquid or a gas. The equation for Bernoulli’s principle is given by,
$P + \dfrac {1}{2} \rho {v}^{2} + \rho gh= constant$ …(1)
Where, P is the pressure exerted by the fluid
$\rho$ is the density of the fluid
$v$ is the velocity of the fluid
$g$ is the gravitational acceleration
$h$ is the height of the container containing fluid
In equation. (1), second term i.e. $\dfrac {1}{2} \rho {v}^{2}$ gives the kinetic energy per unit volume and the third term i.e. $\rho gh$ gives the gravitational potential energy per unit volume. As the addition of both these terms is constant, the energies are conserved.
Hence, Bernoulli’s theorem is a consequence of the law of conservation of energy.

So, the correct option is C i.e. energy.

Note:
Bernoulli’s theorem is ideally applied to incompressible fluids only. The conservation of energy is an assumption. When the fluid flows from one point to another, there is some loss in the energy due to the internal friction. Thus, for a compressible fluid, elastic energy has to be added to Bernoulli's equation. Bernoulli’s equation at constant depth is given by,
${P}_{1} + \dfrac {1}{2} \rho {v}_{1}^{2}={P}_{2} + \dfrac {1}{2} \rho {v}_{2}^{2}$
This equation is applicable for only a small volume of fluid.