Fire hoses used in major structure fires have inside diameters
of 6.0 cm. Suppose such a hose carries a flow of 40.0 L/s starting
at a gauge pressure of 2.2×106 N/m2. The hose goes 10.0 m up a
ladder to a nozzle having an inside diameter of 2.8 cm.
a. What is the pressure in the nozzle?
b. What is the speed of water coming out of the
nozzle?
a)
V = Volume flow rate = 40 L/s = 40 x 10-3 m3/s
dn = diameter of nozzle = 2.8 cm = 0.028 m
An = area of cross-section of the nozzle = (0.25) dn2 = (0.25) (3.14) (0.028)2 = 0.00061544 m2
vn = speed of water coming out of nozzle = ?
Volume flow rate is given as
V = An vn
(40 x 10-3) = (0.00061544) vn
vn = 65 m/s
dh = diameter of hose = 6 cm = 0.06 m
Ah = area of cross-section of the hose = (0.25) dh2 = (0.25) (3.14) (0.06)2 = 0.002826 m2
vh = speed of water coming out of hose = ?
Volume flow rate is given as
V = Ah vh
(40 x 10-3) = (0.002826) vh
vh = 14.2 m/s
Ph = gauge pressure at hose = 2.2 x 106 Pa
Pn = gauge pressure at nozzle
h1 = 0
h2 = 10 m
Using Bernoulli's theorem
Ph + g h1 = Pn + g h2
2.2 x 106 + (1000) (9.8) (0) = Pn + (1000) (9.8) (10)
Pn = 2.102 x 106 Pa
Fire hoses used in major structure fires have inside diameters of 6.0 cm. Suppose such a...
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