Question

A rectangular tank is 225 m by 162 m at the base. With what speed must water flow into it through an aperture 60 cm by 40 cm that the level may be raised 20 cm in 5 hours?

Answer 1

this is the answer in short and easy way

Answer 2

Answer:

•°• Volume of the water flows into the tank in 5 hours = $\sf{225×162×}$$\sf\left(\frac{20}{100}\right)$$\sf{m^3}$

$\implies$ Volume of the water that flows into the tank in one hr

= $\sf\large\frac{1}{5}×$$\sf\large{225×162×}$$\sf\large\frac{20}{100}m^3$

= 1458 m³................ (i)

Area of the cross-section of aperture

= $\sf\large\frac{60}{100}×$$\sf\large\frac{45}{100}m^2$$\sf\large\frac{27}{100}m^2$

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Let the speed of the water be x metres per hour. Then,

Volume of the water flow into the tank in one hour

= (area of cross-section of aperture) × (speed in metre per hour)

= $\sf\left(\frac{27}{100}×x\right)$......... (ii)

__________________

From (i) and (ii), we have,

$\sf\frac{27}{100}×x=1458$

=> x=$\sf\frac{1458×100}{27}m/hr$

= x = 5400 m/hr