Question:
The volume flow rate of fluid in a gas pipe is given by the integral:
The gas pipe is experiencing a leak. The coordinates of a point on a curve of discharged gas at a particular instant are given below:
The plane figure bounded by the curve, the x-axis and the ordinates at x = 0 and x = 8, rotates through a complete revolution about the x-axis. Estimate the volume of gas present using a strip method.
Answer:
Find the areas for each of the ordinates between x = 0 and x = 8.
The first ordinate is found through:
A table of all areas for all ordinates is found below:
Now we have the cross-sectional areas we can apply Simpson's rule for volumes.
Simpson's rule is as follows:
Simpson's rule provides us with an approximate value for the volume of gas.