Question

The town of Hana on the island of Maui maintains a large tank with an open top, containing water for emergencies. The water can drain from the tank through a hose of diameter 8.70 cm. The hose ends with a nozzle of diameter 2.90 cm. A rubber stopper is inserted into the nozzle. The water level in the tank is kept 8.50 m above the nozzle. (a) Calculate the friction force exerted on the stopper by the nozzle. (b) The stopper is removed. What mass of water flows from the nozzle in 1.50 h? (c) Calculate the gauge pressure of the flowing water in the hose just behind the nozzle

Answer 1

  a) the friction force must equal the force of the water behind it; the force due to the water is

force = pressure x area =5502.13N

for the area, use the area of the nozzle = pi (0.029/2)^2

for the pressure, use P = rho g h = 1000kg/m^3 x 9.8m/s/s x 8.50m (rho is the density of the fluid, g the accel due to gravity and h the height of the water above the nozzle level)

b)And the mass flow rate would equal the density times the flow rate, and the mass flow rate is also the mass of water (m) over a given time (t).

m/t = Q * rho

m/t = V * A * rho

m = V * A * rho * t

v = Sqrt[2 g h] = Sqrt[2 x 9.8m/s/s x 8.5m]

the mass flow rate=46038.073Kg