Water is flowing in a streamline motion through a horizontal tube. The pressure at a point in the tube is P where the velocity of now is v. At another point, where the pressure is P/2, the velocity of flow is: (density of water=ρ)

Explanation

In a horizontal flow, Bernoulli's equation states that the sum of the pressure energy and kinetic energy per unit volume is constant. Therefore, if the pressure drops from P to P/2, the kinetic energy (and thus the velocity) must increase to conserve energy. The correct expression for velocity at the point where pressure is P/2 is derived by setting up the equation: P + 1/2 (ρv2) = P/2 + 1/2 (ρv12)Solving for v1 gives us the correct velocity: v1 = √(v2 + P/ρ).Option A correctly reflects this relationship, while the other options either overestimate or underestimate the velocity change due to pressure drop.