You are going to wash the skylights in your kitchen. The skylights are 8.4 m abo

Question

You are going to wash the skylights in your kitchen. The skylights are 8.4 m above the ground. You connect two garden hoses together-a 0.80-cm-radius hose to a 1.0-cm-radius hose. The smaller hose is held on the roof of the house and the wider hose is attached to the faucet on the ground. The pressure at the opening of the smaller hose is 1 atm, and you want the water to have the speed of 6.2 m/s .

1. What should be the speed at ground level in the large hose?

2. What should be the pressure at ground level in the large hose?

Explanation / Answer

radius r1 = 0.8 cm = 0.008 m

radius = r2 = 1 cm = 0.01 m

v1 = 6.2 m/s

p1 = 1 atm

h1 = 8.4 m

h2 = 0

1)

from equation of continuity

A1*v1 = A1*v2

A1 = pi*r1^2

A2 = pi*r2^2

r1^2*v1 = r2^2*v2

0.008^2*6.2 = 0.01^2*v2

v2 = 3.968 m/s

-------------

2)

from Bernoillis theorem

P1 + 0.5*rho*v1^2 + rho*g*h1 = P2 + 0.5*rho*v2^2 + rho*g*h2

10^5 + (0.5*1000*6.2^2) + (1000*9.8*8.4) = P2 + (0.5*1000*3.968^2)+0

P2 = 1.94*10^5 Pa = 1.93 atm <<------------answer

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