MEDIUMUPES B.Tech Admissions 2025
Ranked #42 among Engineering colleges in India by NIRF | Highest CTC 50 LPA , 100% Placements
Equation Of Continuity - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
-
Equation of Continuity is considered one of the most asked concept.
-
12 Questions around this concept.
Solve by difficulty
Water from a tap emerges vertically down with an initial speed of 1.0m/s. The cross-sectional area of a tap is . Assume that the pressure is constant throughout the stream of water and that the flow is steady. The cross-sectional area of the stream 0.15m below the tap is-
The level of water in a tank is 5m in height. A hole of area 1 is made at the bottom of the tank. the rate of leakage of water from the whole is-
Water is flowing through two horizontal pipes of different diameters which are connected. The diameter of the two pipes is 3cm and 6cm respectively. If the speed of water in the narrower tube is 4m/s. Then the speed of water in the wide tube is-
Also Check: Crack JEE Main 2025 - Join Our Free Crash Course Now!
JEE Main 2025: Sample Papers | Syllabus | Mock Tests | PYQs | Video Lectures
JEE Main 2025: Preparation Guide | High Scoring Topics | Study Plan 100 Days
In the given figure, the velocity will be
A container has a small hole at its bottom. The area of cross-section of the hole is A1 and that of the container is A2 . The liquid is poured into the container at a constant rate Q m3/s. The maximum level of liquid in the container will be:
From shows how the stream of water emerging from faucet neeks down as it falls. The area changes from to A through a fall of h. At what rate does the water flow the tap?
A cylindrical tank has a hole of 1m at its bottom. If the water is allowed to flow into the tank from a tube above it at a rate of 70cm3/s, the maximum height upto which the water can rise in the tank is:
From shows how the stream of water emerging from faucet neeks down as it falls. The area changes from to A through a fall of h. At what rate does the water flow the tap?
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 Mass of the liquid entering per second at $\mathrm{A}=\dot{M}_A$
And 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 $B$ be $a_1$ and $a_2$ respectively.
And 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 $\rho_2$ be the densities of the liquid at point 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 flow is incompressible so $\rho_1=\rho_2$
So Equation of Continuity for the liquid flow in tube AB is given by
$$
\begin{gathered}
a_1 v_1=a_2 v_2 \\
\text { or } \quad \text { av }=\text { constant }
\end{gathered}
$$
Or the Equation of Continuity states that for the liquid flow in the tube, the product of cross-section area and velocity remains the same at all points in the tube.
From the Equation of Continuity, we can say that
-
The velocity of flow will increase if cross-section decreases and vice-versa.
Study it with Videos
Equation of Continuity"Stay in the loop. Receive exam news, study resources, and expert advice!"
Books
Reference Books
Clear your Basics with NCERT
E-books & Sample Papers
Get Answer to all your questions
JEE Main Articles
Dec 19, 2024
Back to top