Question

Water flows straight down from an open faucet. The cross-sectional area of the faucet is 2.3 × 10-4m2 and the speed of the water is 0.65 m/s as it leaves the faucet. Ignoring air resistance, find the cross-sectional area of the water stream at a point 0.09 m below the faucet.

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Density of water = = 1000 kg/m³

Pressure of water as it leaves the faucet = P₁ = P_atm (Open to air)

Cross-sectional area of the faucet = A₁ = 2.3 x 10^-4 m²

Speed of the water as it leaves the faucet = V₁ = 0.65 m/s

Pressure of water 0.09m below the faucet = P₂ = P_atm (Open to air)

Cross-sectional area of water 0.09 m below the faucet = A₂

Speed of the water at 0.09 m below the faucet = V₂

Height of the faucet above which we are observing = H = 0.09 m

By bernoulli's equation,

V₂ = 1.479 m/s

By continuity equation,

A₁V₁ = A₂V₂

(2.3x10^-4)(0.65) = A₂(1.479)

A₂ = 1.555 x 10^-4 m²

Cross-sectional area of the water stream at a point 0.09 m below the faucet = 1.555 x 10^-4 m²