An incompressible fluid (water) is flowing through a pipe of diameter 20 cm with
velocity 1.28 m/s. The pressure at this point is 582 kPa. The pipe then narrows to 3
cm diameter and the velocity increases to 30.6 m/s. What is the pressure in the pipe
at this point?

115 kPa

Explanation:

Use Bernoulli equation:

P₁ + ½ ρ v₁² + ρgh₁ = P₂ + ½ ρ v₂² + ρgh₂

Assuming no elevation change, h₁ = h₂.

P₁ + ½ ρ v₁² = P₂ + ½ ρ v₂²

Plugging in values:

(582,000 Pa) + ½ (1000 kg/m³) (1.28 m/s)² = P + ½ (1000 kg/m³) (30.6 m/s)²

P = 115,000 Pa

P = 115 kPa

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