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3 November, 14:06

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?

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  1. 3 November, 16:22
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    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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