A flat plate orifice of 2 in. diameter is located at the end of a 4-in. diameter pipe. Water flows through the pipe and orifice at 2 ft3/s.

Question

A flat plate orifice of 2 in. diameter is located at the end of a 4-in. diameter pipe. Water flows through the pipe and orifice at 2 ft3/s. The diameter of the water jet downstream from the orifice is 1.5 in. Calculate the external force required to hold the orifice in place. Neglect friction on the pipe wall.

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Edana Edana 3 years 2021-08-16T00:43:06+00:00 1 Answers 86 views 0

Answers ( )

  1. thuthuy
    0
    2021-08-16T00:44:22+00:00
    Reply

    Answer:

    =- 1.969*10^3lbf

    Explanation:

    Given that:

    Gage pressure at the inlet P_{gl} = 20psig

    Inlet diameter D = 4 in

    Exit diameter d = 1.5 in

    Volumetric flow rate at inlet

    Q_1 = 2ft³?s

    Applying continuity and the x component of the momentum;

    we have:

    Q = V_1A_1

    V_1A_1 = V_2A_2

    V_1=\frac{Q}{A_1}

    A_1= \pi \frac{D_1^2}{4}

    A_2= \pi \frac{D_2^2}{4}

    Velocity at inlet is calculate as :

    V_1= \frac{4*Q}{ \pi D_1^2}

    V_1= (\frac{4*2}{\pi *4^2})(\frac{144}{1} )

    = 22.92 ft/s

    Velocity at the exit:

    V_2= \frac{4*Q}{ \pi D_2^2}

    V_2= (\frac{4*2}{\pi *1.5^2})(\frac{144}{1} )

    = 162.98 ft/s

    The required external force can be calculated by using the formula:

    R_x+P_{gl}A_l + \rho Q(V_2-V_1)

    R_x=- P_{gl}A_l + \rho Q(V_2-V_1)

    R_x=- (200)(\pi \frac{4^2}{4})+(1.94)(2)(162.98-22.92)

    R_x=- 1969.84

    R_x=- 1.969*10^3lbf

    Thus, the external force required to hold the orifice in place=- 1.969*10^3lbf

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