A 100-m^3 open tank contains water 3 m deep. A. What is the pressure on the water at the bottom of the tank, relative to atmospheric pressure? B. If a hole is drilled in the bottoms of the tank, what is the velocity at which a water jet issues from the hole?

Explanation:

A) Gauge pressure is:

P = ρgh

P = (1000 kg/m³) (9.8 m/s²) (3 m)

P = 29,400 Pa

B) Using Bernoulli equation:

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

ρgh₁ = ½ ρ v₂²

gh₁ = ½ v₂²

v₂ = √(2gh₁)

v₂ = √(2 × 9.8 m/s² × 3 m)

v₂ = 7.67 m/s

Notice you get the same equation using conservation of energy.

KE = PE

½ mv² = mgh

v = √(2gh)

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