Posted by JJ on .
Water flows in a cylindrical, horizontal pipe. As the pipe widens to twice its initial diameter the pressure in the pipe changes.
Calculate the change in pressure between the wide and narrow regions of the pipe. Give your answer as an expression in terms of the density of water, rho, and initial speed v.
The incompressible continuity equation
(Area)*(velocity) = constant
tells you that the speed is 1/4 as high in the wider section. Thus v' = v/4 is the new velocity.
Use the Bernoulli equation to complete the problem. The pressure increase equals the decrease in (1/2)(rho)V^2
Show your work if you need additional assistance.