Question

water flows at a speed of 0.5m/s through a hose with a radius of 0.02m. The hose is horizontal.a) at what speed does the nozzle that has an effective radius of 3.0×10^-3m ? b) what must be the absolute pressure of the water entering the hose if the pressure at the nozzle is atmospheric pressure?

Answer 1

Using the continuity equation we have

A1v1 = A2v2

pi*0.02^2 * 0.5 = pi*(3*10^-3)^2 * v2

v2 = 22.22

so the speed at the nozzle = 22.22 m/s

b) By Bernoulli's equation we have

P1 + 0.5pv1^2 = P2 + 0.5pv2^2

P1 + 0.5*1000*0.5^2 = 101325 + 0.5*1000*22.22^2

P1 = 3.48*10^5 Pa

= 3.48*10^5 / 1.01325*10^5 = 3.435 atm