Question

How many liters of water flow out of pipe of cross section area \[{\text{5c}}{{\text{m}}^{\text{2}}}\] in \[{\text{1minute}}\], if the speed of the water in the pipe is \[{\text{30cm/s}}\].
A. \[{\text{9 litres}}\]
B. \[{\text{8 litres}}\]
C. \[{\text{7 litres}}\]
D. None of the above.

Answer 1

Hint: Firstly calculate the flow of volume per unit time from then we can use unit conversion of \[{\text{1litre = 1000c}}{{\text{m}}^{\text{3}}}\] and then multiply it with the given time in order to obtain your final answer.

Complete step by step answer:

As per the given data,
Speed of water flow is \[{\text{30cm/s}}\].
Area of pipe is \[{\text{5c}}{{\text{m}}^{\text{2}}}\]
So, flow of volume of water per unit time will be \[{\text{30$\times$5= 150c}}{{\text{m}}^{\text{3}}}{\text{/s}}\]
As per the unit conversion \[{\text{1litre = 1000c}}{{\text{m}}^{\text{3}}}\]so,
Volume flow per unit time \[\dfrac{{{\text{150}}}}{{{\text{1000}}}}{\text{litre/s}}\]\[{\text{ = 0}}{\text{.15litre/s}}\]
And hence the water flows for \[{\text{1min = 60sec}}\]. So the total water that will pass the cross section is
\[{\text{ = 0}}{\text{.15}} \times 60{\text{ = 9litres}}\]
Hence, option (a) is our required answer.

Note: The volumetric flow rate can be calculated as the product of the cross-sectional area (A) for flow and the average flow velocity (v). If the area is measured in square feet and velocity in feet per second.
Always write proper units and remember important conversions, as \[{\text{1litre = 1000c}}{{\text{m}}^{\text{3}}}\].