(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 in a horizontal tube (see figure). The pressure of water changes by $700 \; Nm^{-2}$ between $A$ and $B$ where the area of cross-section are $40 \; cm^{2}$ and $20 \; cm^{2},$ respectively. Find the rate of flow of water through the tube in $cm^{3} / s$. (Density of water $= 1000 \; kgm^{-3}$)

DifficultJEE MAIN 2020

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What is a venturi-meter? Explain its construction and working.

Medium

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Water is flowing through a channel (lying in a vertical plane) as shown in the figure. Three sections $A, B$ and $C$ are shown. Sections $B$ and $C$ have equal area of cross-section. If $P_A, P_B$ and $P_C$ are the pressures at $A, B$ and $C$ respectively,then:

Medium

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$Assertion :$ The velocity of flow of a liquid is smaller when pressure is larger and vice-versa.
$Reason :$ According to Bernoulli's theorem,for the stream line flow of an ideal liquid,the total energy per unit mass remains constant.

EasyAIIMS 2013

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Water is flowing through a horizontal tube having cross-sectional areas of its two ends as $A$ and $A'$ such that the ratio $A/A'$ is $5$. If the pressure difference of water between the two ends is $3 \times 10^5 \, N \, m^{-2}$,the velocity of water with which it enters the tube will be ......... $m \, s^{-1}$ (neglect gravity effects).

DifficultAIEEE 2012

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What is a venturi-meter? Explain its construction and working.

Water is flowing through a channel (lying in a vertical plane) as shown in the figure. Three sections $A, B$ and $C$ are shown. Sections $B$ and $C$ have equal area of cross-section. If $P_A, P_B$ and $P_C$ are the pressures at $A, B$ and $C$ respectively,then:

$Assertion :$ The velocity of flow of a liquid is smaller when pressure is larger and vice-versa.$Reason :$ According to Bernoulli's theorem,for the stream line flow of an ideal liquid,the total energy per unit mass remains constant.

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$Assertion :$ The velocity of flow of a liquid is smaller when pressure is larger and vice-versa.
$Reason :$ According to Bernoulli's theorem,for the stream line flow of an ideal liquid,the total energy per unit mass remains constant.