JEE Main 2024 · 8 April · morning · Single correct · +4 / −1
Correct Bernoulli's equation is (symbols have their usual meaning) :
- (a) P+1/2 ρ g h+1/2 ρ v²= constant
- (b) P+m g h+1/2 m v²= constant
- (c) P+ρ g h+ρ v²= constant
- (d) P+ρ g h+1/2 ρ v²= constant
Answer and solution
Answer (d) P+ρ g h+1/2 ρ v²= constant
Solution
Physics sir · 2 steps
Every term in Bernoulli's equation is a pressure, that is, energy per unit volume. Check each term's units.
- Energy per volume. Bernoulli's theorem is energy conservation for a moving fluid, written per unit volume. Take kinetic energy 1/2mv² and potential energy mgh, then divide by volume V, using m/V = ρ.
P + ρ g h + 1/2ρ v² = constant
Term Where it comes from Units P pressure, work done per unit volume N m⁻² ρ g h mgh/V, no factor of 1/2 N m⁻² 1/2ρ v² (1/2mv²)/V, the 1/2 stays N m⁻² - So. Only (d) has ρ g h with no half and 1/2ρ v² with the half, so (d) is the correct form.
The idea to keep. Bernoulli's equation is the energy equation divided by volume. Replace m by ρ in mgh and 1/2mv², and every term becomes a pressure.
Answer from the NTA final answer key. Solution by PrepWiser.