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 45 cm so that the level may be raised 20 cm in 5 hours ?
Answer: Option C
Volume flown in 5 hours :
$$\eqalign{
& = \left( {225 \times 162 \times \frac{{20}}{{100}}} \right){{\text{m}}^3} \cr
& = 7290\,{{\text{m}}^3} \cr} $$
Volume flown in 1 hour :
$$\eqalign{
& = \left( {\frac{{7290}}{5}} \right){{\text{m}}^3} \cr
& = 1458\,{{\text{m}}^3} \cr} $$
∴ Required speed :
$$\eqalign{
& = \left( {\frac{{1458}}{{0.60 \times 0.45}}} \right){\text{m/hr}} \cr
& = 5400\,{\text{m/hr}} \cr} $$
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Volume flown in 5 hours :
$$\eqalign{
& = \left( {225 \times 162 \times \frac{{20}}{{100}}} \right){{\text{m}}^3} \cr
& = 7290\,{{\text{m}}^3} \cr} $$
Volume flown in 1 hour :
$$\eqalign{
& = \left( {\frac{{7290}}{5}} \right){{\text{m}}^3} \cr
& = 1458\,{{\text{m}}^3} \cr} $$
∴ Required speed :
$$\eqalign{
& = \left( {\frac{{1458}}{{0.60 \times 0.45}}} \right){\text{m/hr}} \cr
& = 5400\,{\text{m/hr}} \cr} $$
Was this answer helpful ?
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