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17 May, 23:28

According to information found in an old hydraulies book, the energy loss per unit weight of fluid flowing through a nozzle connected to a hose can be estimated by the formulah = (0.04 to 0.09) (D/d) ^4*V^2/2*g where h is the energy loss per unit weight, D the hose diameter, d the nozzle tip diameter, V the fluid velocity in the hose, and g the acceleration of gravity. do you think this equation is a valid in any system units? Explain.

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  1. 17 May, 23:34
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    Yes equation is valid.

    Explanation:

    Given:

    h = (0.04 to 0.09) (D/d) ^4*V^2/2*g

    Using SI units to assign dimensions to every quantity as follows:

    Energy loss per unit weight h = J / N = kg m ^2 s^-2 / kg m s^-2 = [m]

    Hose diameter D = [m]

    Nozzle tip diameter d = [m]

    Fluid velocity in the hose V = [ m s^-1 ]

    Acceleration of gravity g = [ m s^-2 ]

    Using the Given Equation and plug the SI units of respective quantities:

    h = (0.04 to 0.09) (D/d) ^4*V^2/2*g

    [m] = (0.04 to 0.09) ([m] / [m]) ^4*[ m s^-1 ]^2/2*[ m s^-2 ]

    Simplify the equation above:

    [m] = (1) ^4 * [ m^2 s^-2 ] / [ m s^-2 ]

    [m] = [m]

    Hence, SI units of RHS of given equation = LHS of given equation, we can say the equation has consistent dimensions.
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