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10 February, 06:03

g The pump inlet is located 1 m above an arbitrary datum. The pressure and velocity at the inlet are 100 kPa and 2 m/s, respectively. The pump exit is located 4 m above the same datum. The pressure and velocity are 500 kPa and 3 m/s, respectively. How much power is required to drive this pump assuming and efficiency of 75%

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  1. 10 February, 09:04
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    The power needed to drive this pump assuming and efficiency of 75% is 1874.0 watts (W)

    Explanation:

    Solution:

    Given that:

    Velocity = 2 m/s

    Pressure = 100 kPa

    The pump exit is = 4 m

    Efficiency 75%

    Thus,

    We apply the method called the Bernoulli's equation between two reservoirs

    p₁ / ps + v₁²/2g + z₁

    =p₂/ps/v₂²/2g + z₂ + hL

    The density of gasoline (pg) is = 680 kg m³

    The gravity of acceleration is known to be = 9.81 m/s²

    So,

    100/680 * 9.81 + 2²/2 * 9.81 + 1 = 500 / 680 * 9.81 + 3²/2 * 9.81 + 4 + hL

    16. 2 = 79.41 + hL

    hl = 79.41 - 16.2

    hL = 63.21 m

    the unit weight of gasoline is (γ) = 680 * 9.81 = 6670.8 m/s

    Now we find the efficiency

    The efficiency (η) = The output power / Input power

    Where hL = H

    The input power = γ * Q * H/0.75

    =6670.8 * 12/3600 * 63.21

    =6670.8 * 0.333 * 63.21

    =6670.8 * 0.2107

    =1405.5/0.75

    The input power = 1874.0 Watts
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