Velocity of water in 6 inch diameter pipe is 5ft s-1. Find the velocity in a 3 inch diameter pipe which connect with it?(both pipes flow full)

Explanation

According to the principle of continuity for incompressible fluid flow, the flow rate (area × velocity) must be conserved across both pipes. The flow rate in the 6-inch pipe is:A1 × V1 = (π/4) × (6/12)^2 × 5And in the 3-inch pipe:A2 × V2 = (π/4) × (3/12)^2 × V2Setting both equal, we have:(π/4) × (6/12)^2 × 5 = (π/4) × (3/12)^2 × V2Simplifying gives V2 = 20 ft/s.Option A (60 ft/s) and Option B (30 ft/s) incorrectly apply the continuity equation, leading to a higher velocity than possible. Option C (40 ft/s) overestimates the velocity change due to the diameter reduction.