A long horizontal hose of diameter 4.2 cm is connected to a faucet. At the other
ID: 2251698 • Letter: A
Question
A long horizontal hose of diameter 4.2 cm is connected to a faucet. At the other end, there is a nozzle of diameter 1 cm. Water squirts from the nozzle at velocity 22 m/sec. Assume that the water has no viscosity or other form of energy dissipation.
1)
What is the velocity of the water in the hose ?
__________ m/s
2)
What is the pressure differential between the water in the hose and water in the nozzle ?
__________ Pa
3)
How long will it take to fill a tub of volume 110 liters with the hose ?
__________ sec
Explanation / Answer
1)
from the continuity principle
A1V1 = A2V2
pi*(4.2^2)*V1 = pi*(1*1)*22
V1 = 22/(4.2*4.2)
V1 = 1.247 m/sec.----velocity of the water in the hose
2)
from the bernoullis equation
P1 +d*g*h1 +1/2*d*V1*v1 = P2 + d*g*h2 + 1/2*d*V2*V2
since they are at the same height
h1 = h2.
P1 - P2 = 1/2*d*[ (V2)^2 - (V1)^2 ].
= 0.5*1000*[ 22^2 - 1.247^2 ]
= 241,222.5 Pa.
pressure difference = 241,222.5 pa.
3)
Volume = A*V*t = 0.11 m3
0.11 = pi*r*r*v*t
0.11 = 3.14*(2.1*10^-3)^2*1.247*t
t = 63.70 seconds.--------------time taken
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.