Water (of density 'o') flows steadily through a horizontal pipe of variable cross-section. If the pressure of water is 'P' at a point where the flow speed is ' V ', then the pressure at another point where the flow speed becomes 3 V is

Step-by-step solution

Using Bernoulli's principle for horizontal flow , the relationship between pressure and velocity at two points is given by P₁ + 1 2 V₁^2 = P₂ + 1 2 V₂^2 along a streamline, where is the fluid density. With P₁ = P and V₁ = V at the first point, and V₂ = 3V at the second point, substitute into the equation: P + 1 2 V^2 = P₂ + 1 2 (3V)^2 Simplify the right-hand side: P + 1 2 V^2 = P₂ + 9 2 V^2 Solve for P₂ : P₂ = P + 1 2 V^2 - 9 2 V^2 = P - 4 V^2 This matches option B . The correct answer is B .