Answer to Question #218831 in Mechanics | Relativity for Emmanuels

Question #218831

 An orifice meter has an orifice of 10 cm diameter and a coefficient of discharge of 0.65. If it fixed in a pipe of 25 cm diameter with flowing oil of 0.8 specific gravity. The pressure difference between the pipe and the orifice is measured by a mercury manometer that gives a reading of

80 cm. determine the flow rate.


1
Expert's answer
2021-07-19T16:03:38-0400

Gives

d0=10cmd_0=10cm

Area a0=π4×102=78.5cm2a_0=\frac{\pi}{4}\times10^2=78.5cm^2

Daimeter of pipe d1=25cmd_1=25cm

Area

a1=π4×252=490.625cm2a_1=\frac{\pi}{4}\times25^2=490.625cm^2

s0=0.8s_0=0.8

Reading of different manometer x=80cm of Mercury


h=x[SgS01]=50×[13.60.81]=800cmh=x [\frac{S_g}{S_0}-1]=50\times [\frac{13.6}{0.8}-1]=800cm

h=800cm Of oil

Rate of flow

Q=cda0a1×2gha12a02Q=c_d \frac{a_0a_1\times \sqrt{2gh}}{\sqrt {a_1^2-a_0^2}}


Q=0.65×78.5×490.625×2×981×490.625490.625278.52Q=0.65\times\frac{78.5\times490.625\times \sqrt{2\times981\times490.625}}{\sqrt {490.625^2-78.5^2}}

Q=0.65×78.5×490.625×981.124484.30=50715.66cm3/secQ=\frac{0.65\times78.5\times490.625\times981.124}{484.30}=50715.66cm^3/sec


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