1.

Water flows through a horizontal pipe of varying cross-section at the rate of 20 litres per minuts , determine the velocity of water at a point where diameter is `4 cm`

Answer» Volume of the water floeing per second `V = 20 liter // min = (20 xx 1000)/(60 xx (100)^(3)) m^(3) s^(-1)`
` = (1)/(3) xx 10^(-3) m^(3) s^(-1)`
Ratio of the pipe `r = (4)/(2) = 2 cm = 0.02 m`
Area of cross section
` a = pi r^(2) = (22)/(7) xx (0.02)^(2) m^(2)`
Let `upsilon` be the velocity of flow of water at the given ,Clearly `V = a upsilon`
or ` (1)/(3) xx 10^(-3) = (22)/(7) xx (0.02)^(2) xx upsilon `
or `upsilon = (7 xx 10^(-3))/(3 xx 22 xx (0.02)^(2)) = 0.2639 ms^(-1)`


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