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Equation Of Continuity MCQ - Practice Questions with Answers

Equation Of Continuity MCQ - Practice Questions with Answers

Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

Equation of Continuity is considered one of the most asked concept.
19 Questions around this concept.

Solve by difficulty

MEDIUM

Water is flowing at a speed of 1.5 ms^-1through a horizontal tube of cross-sectional area 10^-2 m² and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force (in N) that you must exert should be (density of water=10³ kgm^-3).

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22.5

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33.7

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Consider the flow is incompressible, which is shown in figure. The magnitude of velocity v is at cross section 3A, 1 m/sec is at cross section 2A, and 4 m/sec is at cross section A. Determine the value of the velocity v

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$\frac{2}{3}$

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The cylindrical tube of a spray pump has a radius R, one end of which has n fine holes, each of radius r. If the speed of flow of the liquid in the tube is V, the speed of ejection of the liquid through the holes is

$\mathrm{\frac{V}{n}\left(\frac{R}{r}\right)^{1 / 2}}$

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$\mathrm{\frac{V}{n}\left(\frac{R}{r}\right)}$

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$\mathrm{\frac{V}{n}\left(\frac{R}{r}\right)^{3 / 2}}$

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$\mathrm{\frac{V}{n}\left(\frac{R}{r}\right)^2}$

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Water is flowing through a tube of radius r with a speed v. If this tube is joined to another tube of radius $\mathrm{r / 2}$ , what is the speed of water in the second tube?

$\mathrm{\frac{v}{4}}$

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$\mathrm{\frac{v}{2}}$

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$\mathrm{2 v}$

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$\mathrm{4 v}$

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A liquid flows through a pipe of varying diameter. The velocity of the liquid is $2 \mathrm{~ms}^{-1}$ at a point where the diameter is $6 \mathrm{~cm}.$ The velocity of the liquid at a point where the diameter is $3 \mathrm{~cm}$ will be

$\mathrm{1 \mathrm{~ms}^{-1}}$

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$\mathrm{4 \mathrm{~ms}^{-1}}$

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$\mathrm{8 \mathrm{~ms}^{-1}}$

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$\mathrm{16 \mathrm{~ms}^{-1}}$

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Which one of the following statements is correct? When a fluid passes through the narrow part of the nonuniform pipe,

its velocity and pressure both increase

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its velocity and pressure both decrease

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its velocity decreases but its pressure increases

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its velocity increases but its pressure decreases

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Water from a tap emerges vertically downwards with an initial speed of $1.0 \mathrm{~ms}^{-1}$ . The cross-sectional area of the tap is $10^{-4} \mathrm{~m}^2$ . Assume that the pressure is constant throughout the stream of water and that the flow is steady. The cross-sectional area of the stream 0.15 m below the tap is: $(take \ g=10 {ms}^{-2} )$

$\mathrm{5.0 \times 10^{-4} \mathrm{~m}^2}$

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$\mathrm{1.0 \times 10^{-5} \mathrm{~m}^2}$

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$\mathrm{5.0 \times 10^{-5} \mathrm{~m}^2}$

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$\mathrm{2.0 \times 10^{-5} \mathrm{~m}^2}$

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A cubical box of wine has a small spout located in one of the bottom corners. When the box is full and placed on a level surface, opening the spout results in a flow of wine with a initial speed of $\mathrm{V}_0$ (see figure). When the box is half empty, someone tilts it at $45^{\circ}$ so that the spout is at the lowest point (see figure). When the spout is opened the wine will flow out with a speed of

$v_0$

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$v_0 / 2$

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$\mathrm{v}_0 / \sqrt{2}$

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$v_0 / \sqrt[4]{2}$

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A large tank is filled with water to a height H. A small hole is made at the base of the tank. It takes $\mathrm{T}_1$ time to decrease the height of water to $\mathrm{H} / \eta,(\eta>1)$ and it takes $\mathrm{T}_2$ time to take out the rest of water. If $\mathrm{T}_1=\mathrm{T}_2$ then the value of $\eta$ is:

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$2 \sqrt{2}$

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Two water pipes $\mathrm{P}$ and $\mathrm{Q}$ having diameters $2 \times 10^{-2} \mathrm{~m}$ and $4 \times 10^{-2} \mathrm{~m}$ , respectively, are joined in series with the main supply line of water. The velocity of water flowing in the pipe $\mathrm{P}$ is

4 times that of Q

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2 times that of Q

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1 / 2 times of that of Q

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1 / 4 times that of Q

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Concepts Covered - 1

Equation of Continuity

It is applied when fluid is an ideal fluid. (means fluid is Incompressible and Non-viscous)

The equation of continuity is derived from the principle of conservation of mass.

Have a look at the flow of ideal fluid through the tube AB.

For the above figure

Let the Mass of the liquid entering per second at $\mathrm{A}=\dot{M}_A$
The mass of the liquid leaving per second at $\mathrm{B}=\dot{M}_B$
From Mass conservation law we can write

$$
\dot{M}_A=\dot{M}_B
$$

If the cross-sectional area of the pipe at points $A$ and $B$ is $a_1$ and $a_2$ respectively.
Let the liquid enter with normal velocity $\mathrm{v}_1$ at A and leave with velocity $\mathrm{v}_2$ at B .
And $\rho_1$ and $\rho_2$ are the densities of the liquid at points A and B respectively.
Then $\dot{M}_A=\rho_1 a_1 v_1$ and $\dot{M}_B=\rho_2 a_2 v_2$
But $\dot{M}_A=\dot{M}_B$
And Since the flow is incompressible so $\rho_1=\rho_2$
So Equation of Continuity for the liquid flow in tube AB is given by

$$
\begin{gathered}
a_1 v_1=a_2 v_2 \\
\text { or } \quad \text { av }=\text { constant }
\end{gathered}
$$

The Equation of Continuity states that for the liquid flow in the tube, the product of cross-section and area remains the same at all points in the tube.

From the Equation of Continuity, we can say that