QJEEM24Ph8f30: JEE Main 2024 Physics - Class 11 JEEM24Ph8f30 Solution: Correct Bernoulli's equation is (symbols have their usual…

Bernoulli's equation relates the pressure, velocity, and height in a flowing fluid and is derived from the principle of conservation of energy. The correct form of Bernoulli's equation is:

$$P+\rho gh+\frac{1}{2}\rho v^2=\text{constant}$$

where:

• P is the pressure within the fluid.
• $\rho$ is the density of the fluid.
• g is the acceleration due to gravity.
• h is the height above a reference point.
• v is the velocity of the fluid.

Looking at the options given:

1. Option A: $$P+\frac{1}{2}\rho gh+\frac{1}{2}\rho v^2=\text{constant}$$
2. Option B: $$P+mgh+\frac{1}{2}m{v}^2=\text{constant}$$
3. Option C: $$P+\rho gh+\rho v^2=\text{constant}$$
4. Option D: $$P+\rho gh+\frac{1}{2}\rho v^2=\text{constant}$$

Option D correctly represents Bernoulli's equation in its proper form. Therefore, the correct answer is:

Option D