posted by Jeremy .
A fire hose 10 cm in diameter delivers water at the rate of 23 kg/s. The hose terminates in a nozzle 3.1 cm in diameter.
(a) What is the flow speed in the hose?
(b) What is the flow speed in the nozzle?
(a) The volume flow rate Q is the mass flow rate divided by the density.
Q = 23/1000 = 0.023 m^3/s
Q = V*A, where A is the cross sectinal area, (pi/4)*D^2 = 10^-2 m^2
and V is the flow speed
V = .023/10^-2 = 2.3 m/s
(b) Q remains contant in the nozzle, but V increases because of the reduction in A. A is reduced by a factor (10/3.1)^2 = 10.4. V increases by the same factor.