Question

A village wishes to measure the quantity of water that is piped to a factory during a typical morning. A gauge on the water line gives the flow rate (in cubic meters per hour) at any instant. The flow rate is about 100 m3/hr at 6 am and increases steadily to about 280 m3/hr at 9 am. Using only this information, give your best estimate of the total volume of water used by the factory between 6 am and 9 am.

Answer 1

Answer:

570 m³

Step-by-step explanation:

The volume of water is the product of flow rate of water and the time taken. We are to get the volume of water used between 6 am and 9 am, that is for 3 hours (9 - 6).

We are given the flow rate at 6 am and the flow rate at 9 am, but this flow rate changes between 6 am and 9 am. To get the estimate of the water used, Let us assume that it flows at the same flow rate as it was at 6 am throughout, hence:

$V_L= 100 m^3/h * 3h=300\ m^3$

Also, let us assume that it flows at the same flow rate as it was at 9 am throughout, hence:

$V_R= 280 m^3/h * 3h=840\ m^3$

To get the best estimate of the total volume, let us find the average of the two values, hence:

$Volume=\frac{V_L+V_R}{2} =\frac{300+840}{2}=570\ m^3$