A tank is full of water. We will use Riemann sum idea to find the work W required to pumpthe water out of the spout as follows. Use 1000 kg/m’ as the weight density of water.3 m
a) A layer of water Ax m thick which lies x m above the bottom of the tank can be assumeda rectangular prism with length 8 m. Use similar triangles to find its width
b) Find the volume of the layer. Give the units.
c) The mass of the layer is approximately equal the weight density of water (1000kg/m”) times its approximate volume. Find the approximate mass of the layer.Give the units.
d) Find the force required to lift this layer of water. (Use 9.8 m/s” for gravity.) Give theunits.e) To be lifted to the top of the pump’s piping, the layer must be lifted a distance equalto 5 – x.
Now find the approximate work W. required to move this layer. Give theunits.f) Now you are ready to set up an integral to find the total work W required to pumpthe water out of the spout. Set up the integral.
g) Compute the integral, and find the total work Wrequired to pump the water out of the spout. Give the units.
