A fire hose 3.8 cm in diameter is capable of spraying water at a velocity of 20 m/s. For a continuous horizontal flow of water, what horizontal force should a fireman exert on the hose to keep it stationary?
I know the answer is 454 N but how does one arrive at this answer?
Cross-section area A= π•d²/4= =3.14•(3.8•10^-2)/4 =1.13•10^-3 m²
As water's density is 1000 kg/m³ and velocity is 20 m/s , ==> the mass of water that passes each second through the unit area of the fire hose cross-section is
1000 kg/m³ •20 m/s =20000 kg/m²•s .
Through the gross section of the fire hose passes
20000 kg/m²•s •1.13•10^-3 m² = 22.7 kg/s.
The fireman has to apply enough force against this to balance the velocity of this mass of water
22.7 • 20 = 453.6 N ≈ 454 N must be applied opposite the water stream direction.