(B) Given:$A_1 = 0.02 \ m^2$,$V_1 = 2 \ m/s$,$P_1 = 4 \times 10^4 \ N/m^2$,$A_2 = 0.01 \ m^2$,$\rho = 1000 \ kg/m^3$.Using the equation of continuity,

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(B) Given:$A_1 = 0.02 \ m^2$,$V_1 = 2 \ m/s$,$P_1 = 4 \times 10^4 \ N/m^2$,$A_2 = 0.01 \ m^2$,$\rho = 1000 \ kg/m^3$.Using the equation of continuity,$A_1 V_1 = A_2 V_2$:$0.02 \times 2 = 0.01 \times V_2 \implies V_2 = 4 \ m/s$.Using Bernoulli's equation for a horizontal tube $(h_1 = h_2)$:$P_1 + \frac{1}{2} \rho V_1^2 = P_2 + \frac{1}{2} \rho V_2^2$$P_2 = P_1 + \frac{1}{2} \rho (V_1^2 - V_2^2)$$P_2 = 4 \times 10^4 + \frac{1}{2} \times 1000 \times (2^2 - 4^2)$$P_2 = 40000 + 500 \times (4 - 16)$$P_2 = 40000 - 6000 = 34000 \ N/m^2 = 3.4 \times 10^4 \ N/m^2$.

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

Medium

Water is flowing steadily through a horizontal tube of non-uniform cross-section. If the pressure of water is $4 \times 10^4 \ N/m^2$ at a point where the cross-section is $0.02 \ m^2$ and the velocity of flow is $2 \ m/s$,what is the pressure at a point where the cross-section reduces to $0.01 \ m^2$?

A
$1.4 \times 10^4 \ N/m^2$
B
$3.4 \times 10^4 \ N/m^2$
C
$2.4 \times 10^4 \ N/m^2$
D
none of these

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Fluid Mechanics and Surface Tension

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Bernoulli's Theorem and Applications of Bernoulli's Theory

Water flows through the tube shown. The cross-sectional areas of the wide and narrow parts are $5 \text{ cm}^2$ and $2 \text{ cm}^2$,respectively. The rate of flow is $500 \text{ cm}^3/\text{s}$. Find the difference in the mercury level of the $U$-tube in $\text{cm}$.

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Why is Bernoulli's equation not applicable to turbulent flow? Explain.

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Air streams horizontally past an airplane. The speed over the top surface is $60 \, m/s$ and that under the bottom surface is $45 \, m/s$. The density of air is $1.293 \, kg/m^3$. The difference in pressure is ....... $N/m^2$.

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$A$ venturimeter has a pipe diameter of $4 \,cm$ and a throat diameter of $2 \,cm$. The velocity of water in the pipe section is $10 \,m/s$. The pressure drop between the pipe section and the throat section is (use density of water $= 1000 \,kg/m^3$):

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Water is flowing through a horizontal pipe of non-uniform cross-section. At the extreme narrow portion of the pipe, the water will have

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Water flows through the tube shown. The cross-sectional areas of the wide and narrow parts are $5 \text{ cm}^2$ and $2 \text{ cm}^2$,respectively. The rate of flow is $500 \text{ cm}^3/\text{s}$. Find the difference in the mercury level of the $U$-tube in $\text{cm}$.

Why is Bernoulli's equation not applicable to turbulent flow? Explain.

Air streams horizontally past an airplane. The speed over the top surface is $60 \, m/s$ and that under the bottom surface is $45 \, m/s$. The density of air is $1.293 \, kg/m^3$. The difference in pressure is ....... $N/m^2$.

$A$ venturimeter has a pipe diameter of $4 \,cm$ and a throat diameter of $2 \,cm$. The velocity of water in the pipe section is $10 \,m/s$. The pressure drop between the pipe section and the throat section is (use density of water $= 1000 \,kg/m^3$):

Water is flowing through a horizontal pipe of non-uniform cross-section. At the extreme narrow portion of the pipe, the water will have

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