A shower head has 20 circular openings, each with radius 1.0mm . The shower head is...
Homework Answers
The concepts used to solve this problem are area of cross section concept and law of continuity of fluid.
Initially, calculate the area of cross section of each circular opening of shower head and area of shower head connected to a pipe by using area of cross section concept. Then, calculate the total area of circular openings of shower head. Finally, determine the speed of water through shower head openings by using law of continuity of fluid.
According to area of cross section concept, the area of circle is the product of 
and square of the radius of the circle.
Here, A is the area of cross section, and r is the radius of the circle.
According to the law of continuity of fluid, the initial flow of fluid is equal to the final flow of fluid.
Here, 
is the total area of the cross section of circular openings of shower head, 
is the speed of water in circular openings of shower head, 
is the area of cross section of shower head is connected to a pipe, and 
is the speed of water in the pipe.
The area of cross section of each circular opening of shower head is given below.
Here, 
is the area of cross section of circular opening of shower head, and 
is the radius of circular opening of shower head.
Substitute 3.14 for 
, 1.0 mm for in the equation and solve for .
Use the following formula to calculate the total area of cross section of circular openings of shower head is,
Here, 
is the number of circular openings.
Substitute 20 for 
, and 
for in the equation and solve for .
Use the following formula to calculate the area of cross section of shower head is connected to a pipe is,
Here, 
is the radius of shower head is connected to a pipe.
Substitute 3.14 for 
, 0.99 cm for , in the equation and solve for .
Use the following relation to determine the speed of water through shower head openings by using law of continuity of fluid.
Substitute 
for, 
for, and 
for 
in the equation and solve for
.
Thus, the speed of water through shower head openings is
.
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