Statement I: When speed of liquid is zero everywhere, pressure difference at any two points depends on equation

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
Given below are two statements:

Statement I: When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $P_{1} - P_{2} = ρ g (h_{2} - h_{1}) .$

Statement II: In venturi tube shown, $2 g h = v_{1}^{2} - v_{2}^{2}$

In the light of the above statements, choose the most appropriate answer from the options given below. [2024]

1 Both Statement I and Statement II are correct.

2 Both Statement I and Statement II are incorrect.

3 Statement I is correct but Statement II is incorrect.

4 Statement I is incorrect but Statement II is correct.

Ans.
(3)

From Bernoulli’s equation

$P_{1} + ρ g h_{1} + \frac{1}{2} ρ v_{1}^{2} = P_{2} + ρ g h_{2} + \frac{1}{2} ρ v_{2}^{2}$

[ $h_{1}$ and $h_{2}$ are height of points from any reference level]

For statement 1:

When speed of liquid is zero everywhere, $v_{1} = v_{2} = 0$

$∴$ $P_{1} - P_{2} = ρ g (h_{2} - h_{1}),$ Hence, statement I is correct.

For statement 2, $h_{1} = h_{2}$

$P_{1} + \frac{1}{2} ρ v_{1}^{2} = P_{2} + \frac{1}{2} ρ v_{2}^{2} \Rightarrow P_{1} - P_{2} = \frac{1}{2} ρ (v_{2}^{2} - v_{1}^{2})$

But, $P_{1} - P_{2} = ρ g h \Rightarrow ρ g h = \frac{1}{2} ρ (v_{2}^{2} - v_{1}^{2})$

Hence, $2 g h = v_{2}^{2} - v_{1}^{2}$ , Hence statement II is incorrect.

Want Us to Email you About Special Offers & Updates?