water flows at a rate of 10m per min through a cylinderical pipe 5mm in diameter . how long would it take to fill a conical vessel whose diameter at the surface 40cm and depth 24 cm?
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Given velocity of flow, V = 10 m/min = 1000 cm/min
Diameter of pipe, D = 5 mm = 0.5 cm
Cross sectional area of pipe, A = π/4 × D^2
= π/4 × (0.5)^2 = 0.0625π cm^2.
Flow rate = A × V = 62.5π cm^3/min.
Radius of vessel = 40/2 = 20 cm
Volume of conical vessel,
Vol = 1/3 × π × (20)^2 × 24 = 3200π cm^3
Time to fill = Vol / Flow rate
= 3200π / 62.5π = 51.2 minutes
Diameter of pipe, D = 5 mm = 0.5 cm
Cross sectional area of pipe, A = π/4 × D^2
= π/4 × (0.5)^2 = 0.0625π cm^2.
Flow rate = A × V = 62.5π cm^3/min.
Radius of vessel = 40/2 = 20 cm
Volume of conical vessel,
Vol = 1/3 × π × (20)^2 × 24 = 3200π cm^3
Time to fill = Vol / Flow rate
= 3200π / 62.5π = 51.2 minutes
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