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Viscous force

A flat plate is moving normal to its plane through a gas under

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Solving time: 4 mins

A flat plate is moving normal to its plane through a gas under the action of a constant force $F$ . The gas is kept at a very low pressure. The speed of the plate $v$ is much less than the average speed $u$ of the gas molecules. Which of the following options is/are true?

SELECT MULTIPLE OPTION

The resistive force experienced by the plate is proportional to

v

At a later time the external force

F

balances the resistive force

The plate will continue to move with constant non-zero acceleration, at all times

The pressure difference between the leading and trailing faces of the plate is proportional to

uv

Views: 5,770 students

Updated on: Apr 20, 2023

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Charlotte Discussed

A flat plate is moving normal to its plane through a gas under the action of a constant force

F

. The gas is kept at a very low pressure. The speed of the plate

v

is much less than the average speed

u

of the gas molecules. Which of the following options is/are true?

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

v_{1} = u + 2 v

Δ V_{1} = (2 u + 2 v)

F_{1} = \frac{d p _{1}}{d t} = ρ A (u + v) \times (2 u + 2 v) = 2 ρ A (u + v)^{2}

v_{2} = (u - 2 v)

Δ v_{2} = 2 u - 2 v

F_{2} = \frac{d p _{2}}{d t} = ρ A (u - v) \times (2 u - 2 v) = 2 ρ A (u - v)^{2}

F_{1}

and

F_{2}

are acting in opposite direction so

F_{n e t} = F_{1} - F - 2 = 2 ρ A (4 uv) = 8 ρ A vu

P = \frac{Δ F}{A} = 8 ρ uv

F_{n e t} = (F - Δ F) = ma

m is the mass of the plate.

F - (8 ρ A uv) = ma

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Question Text	A flat plate is moving normal to its plane through a gas under the action of a constant force $F$ . The gas is kept at a very low pressure. The speed of the plate $v$ is much less than the average speed $u$ of the gas molecules. Which of the following options is/are true?
Updated On	Apr 20, 2023
Topic	Mechanical Properties of Fluids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 4
Upvotes	394
Avg. Video Duration	6 min

A flat plate is moving normal to its plane through a gas under the action of a constant force $F$ . The gas is kept at a very low pressure. The speed of the plate $v$ is much less than the average speed $u$ of the gas molecules. Which of the following options is/are true?

Text solutionVerified

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A flat plate is moving normal to its plane through a gas under the action of a constant force F. The gas is kept at a very low pressure. The speed of the plate v is much less than the average speed u of the gas molecules. Which of the following options is/are true?

Text solutionVerified

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A flat plate is moving normal to its plane through a gas under the action of a constant force $F$ . The gas is kept at a very low pressure. The speed of the plate $v$ is much less than the average speed $u$ of the gas molecules. Which of the following options is/are true?