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Question
Water flows, at 9 km per hour, through a cylindrical pipe of cross-sectional area 25 cm2. If this water is collected into a rectangular cistern of dimensions 7.5 m by 5 m by 4 m; calculate the rise in level in the cistern in 1 hour 15 minutes.
Solution
Rate of flow of water = 9 km/hr
Water flow in 1 hour 15 minutes
i.e. in `5/4 hr = 9 xx 5/4`
= `45/4 km`
= `45/4 xx 1000`
= 11250 m
Area of cross-section
= 25 cm2
= `25/10000 m^2`
= `1/400 m^2`
Therefore, volume of water
= `1/400 xx 11250`
= 28.125 m3
Dimensions of water tank = 7.5 m × 5 m × 4 m
Area of tank = l × b
= 7.5 × 5
= 37.5 m2
Let h be the height of water then,
37.5 × h = 28.125
`h = 28.125/37.5`
= 0.75 m
= 75 cm
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