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Question 4.1: A pipe having diameter 30 cm at a section carries oil of spe......

A pipe having diameter 30 cm at a section carries oil of specific gravity 0.8 at a velocity of 2 m/s. At another section, the diameter is 20 cm. Find the velocity at this section and also the mass rate of flow of the oil.

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Given D_{1} = 30 cm = 0.3 m, D_{2}= 20 cm = 0.2 m, Specific gravity of oil s = 0.8 and V_{1}= 2 m/s
From continuity Eq. (4.3), we have

Q=A_{1}V_{1}=A_{2}V_{2}

Or                                                \frac{\pi }{4}D^{2}_{1}\times2=\frac{\pi }{4}D^{2}_{2}\times V_{2}

Or                                                  V=(\frac{D_{1} }{D_{2} } )^{2}\times2=(\frac{0.3}{0.2} )^{2}\times 2=4.5  m/s

Mass rate of flow of oil =\rho _{\omicron }A_{1}V_{1}

                                =0.8\times 1000\times \frac{\pi }{4}\times(0.3)^{2}\times 2=113.097  kg/s

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