A pipe of diameter 64mm discharges water at a rate of 2.05mm/s into an empty cylindrical tank of diameter 7.6cm and height 2.3m. Find the time required to fill the tank, giving your answer correct to the nearest minute.

Question

Mathematics

Armani Hall

7 February, 18:37

A pipe of diameter 64mm discharges water at a rate of 2.05mm/s into an empty cylindrical tank of diameter 7.6cm and height 2.3m. Find the time required to fill the tank, giving your answer correct to the nearest minute.

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Answers (1)

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Abby Foley · Answer 1

Diameter of pipe = D = 64mm

cross sectional Area of pipe = A = pi * (D/2) ^2 = pi * (32) ^2 = 1024pi mm^2

Discharge Rate of water = v = 2.05 mm/s

Volume of Cylinder = V = pi * (D/2) ^2 * h = pi * (38) ^2 * 2300 = 3321200pi mm^3

(Area of pipe) * (Rate) = (Volume) / (Time)

Time = T = (Volume) / [ (Area of pipe) * (Rate) ]

= (3321200pi) / (1024pi * 2.05)

= 1582.126524s