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Mechanical Properties of Fluids

Energy Associated with a Moving Fluid

Steady flow of water is happening through a pipe of variable c

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Solving time: 4 mins

Steady flow of water is happening through a pipe of variable cross-section. Area of cross-section of the pipe at $A$ and $B$ are $A_{1} = 4 \times 1 0^{- 3} m^{2}$ and $A_{2} = 8 \times$ $1 0^{- 3} m^{2}$ respectively. Height of pipe at $A$ and $B$ above the reference level is $2 m$ and $5 m$ . Speed of flow at $A$ is $v_{1} = 1 ms^{- 1}$ . Density of water is $1 0^{3} kgm^{- 3}$ . Find work done by surrounding liquid on a liquid element of unit volume as it moves from $A$ to $B$ . $[g = 10 ms^{- 2}$ ]

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Book:

Physics for JEE Main and Advanced Mechanics 2 (McGraw Hill)

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Noah Discussed

Steady flow of water is happening through a pipe of variable cross-section. Area of cross-section of the pipe at

A

and

B

are

A_{1} = 4 \times 1 0^{- 3} m^{2}

and

A_{2} = 8 \times

1 0^{- 3} m^{2}

respectively. Height of pipe at

A

and

B

above the reference level is

2 m

and

5 m

. Speed of flow at

A

v_{1} = 1 ms^{- 1}

. Density of water is

1 0^{3} kgm^{- 3}

. Find work done by surrounding liquid on a liquid element of unit volume as it moves from

A

B

[g = 10 ms^{- 2}

]

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

W = Δ U + Δ K = ρ g (h_{2} - h_{1}) + \frac{1}{2} ρ (v_{2}^{2} - v_{1}^{2})

Since,

A_{2} v_{2} = A_{1} v_{1} ∴ v_{2} = \frac{v _{1}}{2} = 0.5 ms^{- 1}

∴ W = 1 0^{3} \times 10 \times (5 - 2) + \frac{1}{2} \times 1 0^{3} \times (0. 5^{2} - 1^{2})

= 3 \times 1 0^{4} - 0.375 \times 1 0^{3} = 29625 J

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Question Text	Steady flow of water is happening through a pipe of variable cross-section. Area of cross-section of the pipe at $A$ and $B$ are $A_{1} = 4 \times 1 0^{- 3} m^{2}$ and $A_{2} = 8 \times$ $1 0^{- 3} m^{2}$ respectively. Height of pipe at $A$ and $B$ above the reference level is $2 m$ and $5 m$ . Speed of flow at $A$ is $v_{1} = 1 ms^{- 1}$ . Density of water is $1 0^{3} kgm^{- 3}$ . Find work done by surrounding liquid on a liquid element of unit volume as it moves from $A$ to $B$ . $[g = 10 ms^{- 2}$ ]
Topic	Mechanical Properties of Fluids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	71

Text solutionVerified

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