Question

Water is streaming downward from a faucet opening with an area of 3.0 x 10-5 m2. It leaves the faucet with a speed of 5.0 m/s. The cross sectional area of the stream 0.50 m below the faucet is:

Answer 1

The cross sectional area of the stream 0.50 m below the faucet is 2.54 x 10⁻⁵ m².

Speed of the water 0.5 m below the faucet

The speed of the water at the lower level is determined using Bernoulli's equation as follows;

P₀ + ρgΔh + ¹/₂ρv₁² = P₀ + 0 +  ¹/₂ρv₂²

ρgΔh + ¹/₂ρv₁²  = ¹/₂ρv₂²

gΔh + ¹/₂v₁²  = ¹/₂v₂²

9.8(0.5) + ¹/₂(5)² = ¹/₂v₂²

2(17.4) = v₂²

34.8 = v₂²

v₂ = √34.8

v₂ = 5.9 m/s

Continuity equation

A₁v₁ = A₂v₂

A₂ = A₁v₁ /v₂

A₂ = (3.0 x 10⁻⁵ x 5) / (5.9)

A₂ = 2.54 x 10⁻⁵ m²

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