Best estimate of the total volume of water used by the factory between 6 am and 9 am

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 70m3/hr at 6 am and increases steadily to about 260m3/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

If the flow rate were expressed as a graph, then it would look like a straight line.  Slope would be (260 -70)/(3-0)

 or 190/3.  The value is approximately 63.3

 

y=63.3 + 70

 

The area under this graph will be the volume of water.  The area will be a combination of a triangle and a rectangle.  We have a rectangle because the y intercept is at 70.

 

260 -70 or 190 will be the change in y value or height.  The 3 hour time difference is the change in x value or base.  The area of the triangle will be one half base times height.  Area will be 0.5*3*190 or 285 cubic meters.

 

The area of the rectangle will be 70*3 or 210 cubic meters..  These will be the sides of the rectangle if you see it on a graph.

 

Total area is 285 + 210 or 495 cubic meters.