MHT CET202616 April 2026Evening ShiftPhysicsMechanical Properties of FluidsActual
A horizontal pipe carries water in a streamline flow. At point along the pipe, where the cross-sectional area is A₁ , the velocity of water is V₁ and the pressure is P₁ . What is the pressure of water at another point where the cross-sectional area is A₂ ?
Options
- AP₁ - V₂^2 2A₁^2 (A₂^2 - A₁^2)
- BP₁ + V₁^2 2A₂^2 (A₂^2 - A₁^2)
- CP₁ V₁^2(A₁^2 - A₂^2)
- DP/ V₁^2 A₂^2
Correct answer
B. P₁ + V₁^2 2A₂^2 (A₂^2 - A₁^2)
Step-by-step solution
Using the equation of continuity: A₁ V₁ = A₂ V₂ V₂ = A₁ V₁ A₂ Using Bernoulli's theorem for a horizontal pipe: P₁ + 1 2 V₁^2 = P₂ + 1 2 V₂^2 P₂ = P₁ + 1 2 (V₁^2 - V₂^2) Substituting the value of V₂ : P₂ = P₁ + 1 2 (V₁^2 - A₁^2 V₁^2 A₂^2 ) P₂ = P₁ + V₁^2 2A₂^2 (A₂^2 - A₁^2)