Question

The area of cross-section of a pipe is $3.5cm^2$ and water is flowing out of the pipe at the rate of 40cm/s. How much water is delivered by the pipe in one minute?

Answer 1

Hint:
Here, we will find the rate of flow of water in the pipe by using the formula of rate of flow of liquid. Then we will find the water delivered in one minute by converting our answer from seconds to minutes.

Formula used:
Rate of flow of water $ = A \times v$, where, $A$ is the area of the container from which water is flowing and $v$ is the velocity of the fluid flowing.

Complete step by step solution:
It is given that,
The area of cross section is $A = 3.5cm^2$
Velocity at which the fluid is flowing out of the pipe is $v = 40cm/s$.
Now, substituting the above value in formula Rate of flow of water $ = A \times v$, we get
Rate of flow of water $ = 3.5 \times 40{\text{c}}{{\text{m}}^3}{\text{/s}}$
Multiplying the terms, we get
$ \Rightarrow $ Rate of flow of water $ = 140{\text{c}}{{\text{m}}^3}{\text{/s}}$
Now, as we got our answer in ${\text{c}}{{\text{m}}^3}{\text{/s}}$ we will multiply it with 60 to get the amount of water delivered from the pipe in one minute because 1 minute is equal to 60 seconds.
Therefore,
Amount flowed in one minute $ = 140 \times 60c{m^3}$
Multiplying the terms, we get
 $ \Rightarrow $ Amount flowed in one minute $ = 8400c{m^3}$

So the amount of water delivered by the pipe in 1 minute is $8400c{m^3}$.

Note:
 The flow rate is different from the velocity. For example, in a river, the more the velocity, the more will be the flow rate but the flow rate also depends on the size of the thing. Here, we need to keep the unit the same throughout the solution because if we change the unit we will get wrong answers.