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14 April, 07:28

Underground water is to be pumped by a 78 percent efficient 5-kW submerged pump to a pool whose free surface is 30 m above the underground water level. The diameter of the pipe is 7 cm on the intake side and 5 cm on the discharge side. Take the density of water to be 1 kg/L = 1000 kg/m3. Assume the elevation difference between the pump inlet and the outlet and the effect of the kinetic energy correction factors to be negligible

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  1. 14 April, 07:39
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    a. Q = 10.15 x 10⁻³ m³/s

    b. Δp = 202.76 kPa

    Explanation:

    For solve the pipe system can use Bernoulli equations:

    Patm / ρ + V₁² / 2 + g Z₁ + e pump / m = P atm / ρ + V₂² / 2 + g Z₂

    e pump / ρ * Q = V₂² / 2 + g Z₂

    a.

    Q = V₂ * A₂

    e pump / ρ * V₂ * A₂ = V₂² / 2 + g Z₂

    Given: e pump = 0.78 * 5 kW = 3.9 kW, ρ = 1000 kg / m³, A₂ = π * 5 ²cm / 4, Z₂ = 30 m

    A₂ = 1.96 x 10 ⁻³ m²

    V₂ = 5.18 m/s

    Q = 10.15 x 10⁻³ m³/s

    b.

    A₁ = π * 7² cm / 4 = 3.85 x 10⁻³ m²

    Δp = ρ * [ (Q / A₁) ² / 2 - (Q / A₂) ² / 2 + e pump / ρ * Q]

    Δp = 202.76 kPa
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