A pipe carrying water is laid out over level ground. One segment of the pipe has a diameter of 2.22 cm and the next segment has a diameter of 1.82 cm. In the wider segment, the water pressure is 83,700 Pa and the water is moving at 2.77m/sec.

Question

1-what is the speed of the water in the narrow segment?
2-what is the pressure of the water in the narrow segment?

I was going to use Bernoulli's equation to find P2 but I wasn't given the density so I'm lost for what to put in place of it. Would this be a place for the law of continuity? anything helps, thank you!!

Answer 1

It is water. The density is 1 gram/cc or 1000 kg/m^3

Q = flow rate , volume/second.
Q is constant, the same amount of water goes by each point each seconds (this is continuity)
therefore
V * area = constant
2.77 * pi (1.11^2) = v * pi (0.91^2)
or
v = 2.77(1.11/0.91)^2
============================
p/rho + (1/2)v^2 = constant
rho is constant here (incompressible fluid)
83700/1000 + (1/2)(2.77)^2 = p/1000 + (1/2)v^2