TS EAMCET · Physics · Mechanical Properties of Fluids

A large storage tank, open to the atmosphere at top and filled with water, develops a small hole in its side at a point $20.0 m$ below the water level. If the rate of flow from the hole is $3.08 \times 10^{- 5} m^{3} s^{- 1}$ , then the diameter of the hole is [Take $g = 10 m s^{- 2}$ ]

A $1.0 mm$
B $1.2 mm$
C $1.4 mm$
D $1.6 mm$

Verified Solution

Answer & Solution

Correct Answer

(C) $1.4 mm$

Step-by-step Solution

Detailed explanation

Velocity of the efflux for an orifice at depth h can be written as, v=2gh=2×10×20=20 m s-1 Now, volume flow rate can be written as, area of orifice×velocity of efflux…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A large storage tank, open to the atmosphere at top and filled with water, develops a small hole in its side at a point 20.0 m below the water level. If the rate of flow from the hole is 3.08×10-5 m3 s-1, then the diameter of the hole is [Take g=10 m s-2]

Step-by-step Solution

A large storage tank, open to the atmosphere at top and filled with water, develops a small hole in its side at a point $20.0 m$ below the water level. If the rate of flow from the hole is $3.08 \times 10^{- 5} m^{3} s^{- 1}$ , then the diameter of the hole is [Take $g = 10 m s^{- 2}$ ]