Question

1. Fluid flows at a rate of 2.0 L/s through a pipe with a diameter of 10 cm. The pipe then goes up a height of 5m while narrowing to a diameter of 5 cm. What is the pressure gradient (the change in pressure) from the top to the bottom of the pipe? [hint: draw this and label with P1, v1, P2, v2 etc.)

2. A hurricane wind blows across the top of a flat roof measuring 12 m by 5m at a speed of 120 km/h.
a) Is the air pressure above the roof higher or lower than the pressure inside the house? Explain.
b) Find the pressure difference.
c) How much force is exerted on the roof? If the roof's structure fails, will in

Answer 1

2. we use Bernoulli's principle to analyze this problem. Since the velocity of fluid is greater above the roof, the pressure is less above the roof; therefore, if the roof fails, the force will be coming from below, and the roof blows out bernoulli's principle gives us

P1 + 1/2 rho v1^2 + rho g h1 = P2 + 1/2 rho v2^2 + rho g h2

subscripts 1 refer to below the roof; 2 above the roof
rho= density of fluid = 1.29 kg/m^3
P=pressure
v=velocity of fluid
h= height of fluid; we will assume the roof is sufficiently thin that we can set h1=h2, so the two terms sum to zero

we have

P1 +0 + rho g h1 = P2 + 1/2 rho v^2 + rho gh 2

P1-P2 = 1/2 rho v2^2 = 1/2 x 1.29 kg/m^3 x (33.33m/s)^2 = 716.67 N/m^2 Ans.

therefore, force = pressure x area = 716.67 N/m^2 x 12mx 5m = 43000.2 N Ans