top of page
ohmymaths

Simpson's Rule for Volumes: Example 1

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.


Recent Posts

See All

Principle Stresses: Example 2

Question: The direct stresses acting on an element of material, on orthogonal planes, are 85N/mm^2 (tensile) and 45N/mm^2 (tensile)...

Eccentric Loading: Example 1

Question: A hole in a pressure vessel end plate repair casting is being drilled using a radial arm drill. The distance from the drill...

Comments


bottom of page