A cylindrical tank with a height h=1 m is filled with water up to its brim. (a) what time is required to empty the tank through an orifice at its bottom it the cross-sectional area of the orifice is 4001 that of tank? (b) Compare this time with that required for the same volume of water to flow out of the tank if the water level in the tank is maintained constant at a height h=1 m from the orifice.

(a) Time taken to empty the tank (has been derlved in theory) is:taA=a2g2AH=400Substituting the values we have,t=2×9.82×4001=180 s=3 min(b) Rate of flow of water Q=a(2gH)= constantTotal volume of water V=AHTIme take to empty the tank with constant ratet=QV=a2gHAH=2×9.8×1400×1=90 s=1.5 min

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Mechanical Properties of Fluids

Applications of Bernoulli's Theorem

A cylindrical tank with a height h=1 {~m} is filled with water

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A cylindrical tank with a height $h = 1 m$ is filled with water up to its brim. (a) what time is required to empty the tank through an orifice at its bottom it the cross-sectional area of the orifice is $\frac{1}{400}$ that of tank? (b) Compare this time with that required for the same volume of water to flow out of the tank if the water level in the tank is maintained constant at a height $h = 1 m$ from the orifice.

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Physics Galaxy Mechanics Vol 1 (Ashish Arora)

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A cylindrical tank with a height

h = 1 m

is filled with water up to its brim. (a) what time is required to empty the tank through an orifice at its bottom it the cross-sectional area of the orifice is

\frac{1}{400}

that of tank? (b) Compare this time with that required for the same volume of water to flow out of the tank if the water level in the tank is maintained constant at a height

h = 1 m

from the orifice.

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

(a) Time taken to empty the tank (has been derlved in theory) is:

t \frac{A}{a} = \frac{2 A}{a 2 g} H = 400

Substituting the values we have,

t = \frac{2 \times 400}{2 \times 9.8} 1 = 180 s = 3 min

(b) Rate of flow of water

Q = a (2 g H) =

constant
Total volume of water

V = AH

TIme take to empty the tank with constant rate

t = \frac{V}{Q} = \frac{A H}{a 2 g H} = \frac{400 \times 1}{2 \times 9.8 \times 1} = 90 s = 1.5 min

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Question Text	A cylindrical tank with a height $h = 1 m$ is filled with water up to its brim. (a) what time is required to empty the tank through an orifice at its bottom it the cross-sectional area of the orifice is $\frac{1}{400}$ that of tank? (b) Compare this time with that required for the same volume of water to flow out of the tank if the water level in the tank is maintained constant at a height $h = 1 m$ from the orifice.
Topic	Mechanical Properties of Fluids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	126

Text solutionVerified

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