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Water (density = 1000 kg/m3) at ambient temperature flows through a horizontal pipe of uniform cross section at the rate of 1 kg/s. If the pressure drop across the pipe is 100 kPa, the minimum power required to pump the water across the pipe, in watts, is_____
    Correct answer is '100'. Can you explain this answer?
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    Calculation of Minimum Power Required to Pump Water Across a Pipe

    Given data:
    - Density of water (ρ) = 1000 kg/m³
    - Mass flow rate of water (m) = 1 kg/s
    - Pressure drop across the pipe (ΔP) = 100 kPa

    Formula:
    - Power (P) = m x ΔP / ρ

    Calculation:
    - P = 1 x 100 / 1000
    - P = 0.1 kW or 100 W

    Explanation:

    The minimum power required to pump water across a pipe can be calculated using the formula P = m x ΔP / ρ, where P is the power in watts, m is the mass flow rate of water in kg/s, ΔP is the pressure drop across the pipe in Pa, and ρ is the density of water in kg/m³.

    In this question, the given mass flow rate of water is 1 kg/s, and the pressure drop across the pipe is 100 kPa, which is equivalent to 100,000 Pa. The density of water is given as 1000 kg/m³.

    Using the formula, we can calculate the minimum power required to pump the water across the pipe as follows:

    P = m x ΔP / ρ
    P = 1 x 100,000 / 1000
    P = 100 W

    Therefore, the minimum power required to pump water across the pipe is 100 watts.
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