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Concepts of Physics

Fluid Mechanics

Suppose the density of air at Madras is _{0} and atmospheric p

Concepts of Physics

Class 11

HC Verma Part I

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In the derivation of

P_{1} - P_{2} = ρ g z

, it was assumed that the liquid is incompressible. Why will this equation not be strictly valid for a compressible liquid?

Suppose the density of air at Madras is

ρ_{0}

and atmospheric pressure is

P_{0}

. If we go up, the density and the pressure both decrease. Suppose we wish to calculate the pressure at a height

10 km

above Madras. If we use the equation

P_{0} - P = ρ_{0} g z

, will we get a pressure more than the actual or less than the actual ? Neglect the variation in

g

. Does your answer change if you also consider the variation in

g

The free surface of a liquid resting in an inertial frame is horizontal. Does the normal to the free surface pass through the centre of the earth? Think separately if the liquid is
(a) at the equator
(b) at a pole
(c) somewhere else.

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Question

Easy

Solving time: 2 mins

Suppose the density of air at Madras is $ρ_{0}$ and atmospheric pressure is $P_{0}$ . If we go up, the density and the pressure both decrease. Suppose we wish to calculate the pressure at a height $10 km$ above Madras. If we use the equation $P_{0} - P = ρ_{0} g z$ , will we get a pressure more than the actual or less than the actual ? Neglect the variation in $g$ . Does your answer change if you also consider the variation in $g$ ?

Name: Video solution 1: [Solved] Suppose the density of air at Madras is ρ0 and atmospheric pressure is P0. If we go up, the density and the pressure both decrease. Suppose we wish to calculate the pressure at a height 10 km above Madras. If we use the equation P0−P=ρ0gz, will we get a pressure more than the actual or less than the actual ? Neglect the variation in g. Does your answer change if you also consider the variation in g? - Concepts of Physics
Uploaded: 2022-09-25T15:40:24.000Z
Duration: 9 min

Views: 6,210 students

Updated on: Sep 25, 2022

Book:

Concepts of Physics (HC Verma Part I)

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Elizabeth Discussed

Suppose the density of air at Madras is

ρ_{0}

and atmospheric pressure is

P_{0}

. If we go up, the density and the pressure both decrease. Suppose we wish to calculate the pressure at a height

10 km

above Madras. If we use the equation

P_{0} - P = ρ_{0} g z

, will we get a pressure more than the actual or less than the actual ? Neglect the variation in

g

. Does your answer change if you also consider the variation in

g

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

Using the equation

P_{0} - P = ρ_{0} g z

, we get:

P = P_{0} - ρ_{o} g z

The pressure calculated by using this equation will be more than the actual pressure because density at a height of 10 km above Madras will be less than

ρ_{0}

.Yes, the answer will change if we also consider the variation in g. Because g decreases with height, it will have the same effect on pressure as that of density.

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Question Text	Suppose the density of air at Madras is $ρ_{0}$ and atmospheric pressure is $P_{0}$ . If we go up, the density and the pressure both decrease. Suppose we wish to calculate the pressure at a height $10 km$ above Madras. If we use the equation $P_{0} - P = ρ_{0} g z$ , will we get a pressure more than the actual or less than the actual ? Neglect the variation in $g$ . Does your answer change if you also consider the variation in $g$ ?
Updated On	Sep 25, 2022
Topic	Mechanical Properties of Fluids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 2
Upvotes	253
Avg. Video Duration	12 min

Text solutionVerified

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