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A shower head has 20 circular opening each of radius 1 mm. Shower head is connected to a pipe of radius 0.8 cm. The speed of water in the pipe is 3ms–1. Find the speed of water as it exists from the shower openings.
  • a)
    7.6 ms–1
  • b)
    9.6 ms–1
  • c)
    5.6 ms–1
  • d)
    3.6 ms–1
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A shower head has 20 circular opening each of radius 1mm. Shower head ...
The correct answer is: 9.6 ms–1
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A shower head has 20 circular opening each of radius 1mm. Shower head ...
To find the volume flow rate of water through the shower head, we need to calculate the total area of all the circular openings and multiply it by the speed of water in the pipe.

The area of each circular opening is given by the formula: A = πr^2, where r is the radius. In this case, the radius is 1mm, which is 0.1cm.

So, the area of each circular opening is A = π(0.1cm)^2 = 0.01π cm^2.

Since there are 20 circular openings, the total area of all the openings is 20 * 0.01π cm^2 = 0.2π cm^2.

The speed of water in the pipe is given as 3 m/s.

To convert the area from cm^2 to m^2, we divide it by 10000: 0.2π cm^2 = (0.2π/10000) m^2.

The volume flow rate (Q) is given by the formula: Q = A * v, where A is the area and v is the velocity.

So, Q = (0.2π/10000) m^2 * 3 m/s = (0.6π/10000) m^3/s.

Therefore, the volume flow rate of water through the shower head is (0.6π/10000) m^3/s.
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A shower head has 20 circular opening each of radius 1mm. Shower head is connected to a pipe of radius 0.8cm. The speed of water in the pipe is 3ms–1. Find the speed of water as it exists from the shower openings.a)7.6ms–1b)9.6ms–1c)5.6ms–1d)3.6ms–1Correct answer is option 'B'. Can you explain this answer?
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