Problem 2: Water is flowing smoothly through a closed pipe system. At one point the speed of water is 3 ms^-1, while at another point 3 meters higher the speed is 4 ms^-1. At the lower point, the pressure is 80 K Pa. Find the pressure at the upper point. Where 1 Nm^-2 = 1 Pa.

Solution

Given data                    At the upper point

                                      Speed of water = v₁ = 4 ms^-1,        (Relative) Height, h₁ = 3 m

                                             At the lower point

                                             Speed of water = v₂ = 3 ms^-1,                       Pressure = P₂ = 80 K Pa = 80000 Pa

                                             Relative height = h₂ = 0 m             

Required                        Pressure at the higher point = P₂ =?

Formula                          For the smooth flow of water, the Bernoulli’s equation is

Put the values

Now we know that density of water is 1000 kg m^-3 and the gravitational acceleration is 9.8 ms^-2. Therefore,