(C) Using Bernoulli's equation for a horizontal Venturi meter: $P_1 - P_2 = \frac{1}{2} \rho v_1^2 \left[ \left( \frac{A}{a} \right)^2 - 1 \right]$.Gi

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(C) Using Bernoulli's equation for a horizontal Venturi meter: $P_1 - P_2 = \frac{1}{2} \rho v_1^2 \left[ \left( \frac{A}{a} \right)^2 - 1 \right]$.Given: Pressure drop $\Delta P = 24 \; Pa$,density of blood $\rho = 1.06 \times 10^3 \; kg/m^3$,$A = 8 \; mm^2$,$a = 4 \; mm^2$.The ratio of areas is $\frac{A}{a} = \frac{8}{4} = 2$.Substituting the values into the equation:$24 = \frac{1}{2} \times 1060 \times v_1^2 \times (2^2 - 1)$$24 = 530 \times v_1^2 \times 3$$24 = 1590 \times v_1^2$$v_1^2 = \frac{24}{1590} \approx 0.01509$$v_1 = \sqrt{0.01509} \approx 0.123 \; m/s$.

Class 11 Physics Fluid Mechanics and Surface Tension Bernoulli's Theorem and Applications of Bernoulli's Theory

Easy

Blood velocity: The flow of blood in a large artery of an anesthetised dog is diverted through a Venturi meter. The wider part of the meter has a cross-sectional area equal to that of the artery,$A = 8 \; mm^2$. The narrower part has an area $a = 4 \; mm^2$. The pressure drop in the artery is $24 \; Pa$. What is the speed (in $m/s$) of the blood in the artery?

A
$0.657$
B
$2.56$
C
$0.123$
D
$1.26$

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Class 11

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Fluid Mechanics and Surface Tension

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Bernoulli's Theorem and Applications of Bernoulli's Theory

In this figure,an ideal liquid flows through a tube of uniform cross-section. The liquid has velocities $v_A$ and $v_B$,and pressures $P_A$ and $P_B$ at points $A$ and $B$ respectively.

Easy

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Glycerine of density $1.25 \times 10^3 \ kg/m^3$ is flowing in a conical-shaped horizontal pipe. The cross-sectional area of the pipe at its two ends is $10 \ cm^2$ and $5 \ cm^2$ respectively. The pressure difference between the two ends is $3 \ N/m^2$. The rate of flow of the liquid in the pipe is:

DifficultMHT CET 2024

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$A$ manometer connected to a closed tap reads $4.5 \times 10^5 \text{ Pa}$. When the tap is opened,the reading of the manometer falls to $4 \times 10^5 \text{ Pa}$. The velocity of the flow of water is ........ $m/s$.

Medium

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$A$ liquid enters at point $A_{1}$ with a speed of $3.5 \ m/s$ and leaves at point $A_{2}$. Find the height attained by the liquid above point $A_{2}$ (in $cm$). (in $.25$)

MediumAIIMS 2019

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Explain blood flow and heart attack with the help of Bernoulli's principle.

Medium

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In this figure,an ideal liquid flows through a tube of uniform cross-section. The liquid has velocities $v_A$ and $v_B$,and pressures $P_A$ and $P_B$ at points $A$ and $B$ respectively.

$A$ manometer connected to a closed tap reads $4.5 \times 10^5 \text{ Pa}$. When the tap is opened,the reading of the manometer falls to $4 \times 10^5 \text{ Pa}$. The velocity of the flow of water is ........ $m/s$.

$A$ liquid enters at point $A_{1}$ with a speed of $3.5 \ m/s$ and leaves at point $A_{2}$. Find the height attained by the liquid above point $A_{2}$ (in $cm$). (in $.25$)

Explain blood flow and heart attack with the help of Bernoulli's principle.

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