Bernoulli's equation: pressure in a narrower pipe
Water (ρ = 1,000 kg/m³) flows through a horizontal pipe at 2 m/s with a pressure of 150 kPa. In a narrower section, it flows at 4 m/s. What is the pressure there?
Answer B: explanation for every choice
A
This leaves out the ½: ρ(v₂² − v₁²) = 12 kPa.
B
Correct. P₂ = P₁ − ½ρ(v₂² − v₁²) = 150 − ½(1,000)(16 − 4) = 150 − 6 = 144 kPa.
C
This uses (v₂ − v₁)² instead of v₂² − v₁².
D
This adds the pressure change instead of subtracting it.
TakeawayHorizontal flow: P₁ + ½ρv₁² = P₂ + ½ρv₂².
Equation usedBernoulli's equation
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