Water flowing through a garden hose of diameter 2.72 cm fills a 20.0 L bucket in
ID: 1564001 • Letter: W
Question
Water flowing through a garden hose of diameter 2.72 cm fills a 20.0 L bucket in 1.50 min. (a) What is the speed of the water leaving the end of the hose? (b) A nozzle is now attached to the end of the hose. If the nozzle diameter is one-third the diameter of the hose, what is the speed of the water leaving the nozzle? A legendary Dutch boy saved Holland by plugging a hole in a dike with his finger, which is 1.10 cm in diameter. (a) If the hole was 1.80 m below the surface of the North Sea (density 1030 kg/m^3), what was the force on his finger? (b) If he pulled his finger out of the hole, how long would it take the released water to fill 1 acre of land to a depth of 1 ft assuming the hole remained constant in size? (A typical U.S. family of four uses 1 acre-foot of water, 1234 m^3, in 1 year.) The Bernoulli effect can have important consequences for the design of buildings. For example, wind can blow around a skyscraper at remarkably high speed, creating low pressure. The higher atmospheric pressure in the still air inside the buildings can cause windows to pop out. As originally constructed, the John Hancock Building in Boston popped windowpanes that fell many stones to the sidewalk below.Explanation / Answer
40)
The cross sectional area of the hose is
A = pi ( d^2/40 = pi ( 2.72 * 10^-2)^2/4 = 0.00057651185 m^2
Q = Av
v= Q/A = 20 L/1.5 min ( 1 min/ 60 s) ( 10^3 cm^3/ 1L) / 0.00057651185 m^2
= 2.22e-4/ 0.00057651185 m^2
=0.38 m/s
(b)
A2/A1 = ( pi ( d2^2/4/ pi d1^2/4) = ( d2/d1)^2 = ( 1/3)^2 = 1/9
A2 = A1/9
from the equation of conitinuity
A1 v1 = A2 v2
v2 = ( A/A2) v1
v2 = (9) 0.38
=3.46 m/s
As per guide lines I worked first problem , please post remaning questions in the next post
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