Question #206531

Three pipes deliver water to a large exit pipe. The velocity at section 2 is 5 ms^{-1}, and the exit flow rate, Q_{4} is 120 m^{3}hr^{-1}. Find the velocities at 1, 3 and 4 if it is known that Q_{3}/Q_{4} = 0.5

Expert's answer

Continuity equation for fixed CV with ID flow and discrete CS's

"0= \\sum m_ {out}- \\sum m_{in}"

where m "= \\rho Q= \\rho VA" , thus

"0=(\\rho Q_4)-( \\rho V_1A_1+\\rho V_2A_2+\\rho V_3A_3)"

Since "Q_3=0.5Q_4"

"V_3= \\frac{Q_4}{0.5A_3}= \\frac{120}{\\frac{\\pi}{2}0.06^2}=5.89 m\/hr"

substituting "V_3"

"0=120 -(V_1 \\frac{\\pi}{4}0.04^2+5 \\frac{\\pi}4 0.05^2+5.98 \\frac{\\pi}40.06^2)"

"V_1=5.43 m\/hr"

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