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Hydraulics

Q1:

The height of water level in a tank above the centre of a circular hole 2.5 cm in diameter is 50 m. The velocity of water flowing through the hole, is

A 31.1 m/sec

B 31.2 m/sec

C 31.3 m/sec

D 31.4 m/sec.

ANS:C - 31.3 m/sec

To find the velocity of water flowing through the hole, we can use Torricelli's theorem, which relates the velocity of fluid flowing out of an opening to the height of the fluid above the opening. Torricelli's theorem is derived from Bernoulli's equation. The formula for the velocity of fluid flowing out of the opening is: v=2gh​ Where:

  • v is the velocity of the fluid,
  • g is the acceleration due to gravity (approximately 9.81 m/s29.81m/s2 on Earth),
  • ℎ is the height of the fluid above the opening.
Given:
  • ℎ=50 mh=50m
We can calculate the velocity v: v=2×9.81×50 v=981 v≈31.32 m/s Therefore, the velocity of water flowing through the hole is approximately 31.32 m/s . Among the given options, the closest one is 31.3 m/s.



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