As shown in the picture, a fire hose carries water from the hydrant to the secon
ID: 1476199 • Letter: A
Question
As shown in the picture, a fire hose carries water from the hydrant to the second floor of a house, flowing out at a point 3.80 m above the hydrant. The hose tapers from a radius of 5.20 cm at the hydrant (point A) to radius 1.20 cm at the tip (point B). The water flows by point A with a speed of 85.0 cm/s. [ recall that, A circle = pi r^2 ] Find the speed of the water at point B. Find the pressure of the water at point A as it leaves the hydrant. (Since point B is in the air, it will be at atmospheric pressure, 1.00 atm.) Compute the volume of water that flows out per second.Explanation / Answer
r1 =5.2 cm , r2 =1.2 cm ,v1 = 85 cm/s
(a) Volume flow rate is constant
A1v1 =A2v2
v2 = (r1/r2)^2v1 = (5.2/1.2)^2(85)
Veloity at point B is v2 = 1596.11 cm/s
(b) P2 =1 atm =101325 Pa
density of water d =1000 kg/m^3 , h =3.8 m
From Bernoullis theorem
P1 +(1/2)dv1^2 = P2+(1/2)dv2^2 +dgh
P1 = P2 +dgh +(1/2)d[v2^2 -v1^2]
P1 =101325 + (1000*9.8*3.8) +(0.5*1000)[(15.9611)^2 - (0.85)^2]
Pressure at Point A is P1 =265582 Pa
(c) volume flow rate = A1v1 = (3.14*5.2*5.2*85)
Volume flow rate =7216.769 cm^3/s
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