MHT-CET Physics Crash Course “Equation of Continuity” Class 12

“Equation of Continuity” MHT-CET Class 12 Physics Crash Course | Chapter Mechanical Properties of Fluids

In this session G.S. Khairnar discussed the theory and MCQ’s of “Equation of Continuity”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.

Equation of Continuity:-

Hello everyone we are familiar about types of flow of fluid. E.g.1. The flow of water in river on plane surface, 2. Flow of water from the peak of mountain like water fall. What do we observe in these examples? Here we notice that the flow of water in 1^st case has constant velocities throughout the motion, whereas the flow of liquid in 2nd has different velocities for all the layers which are beyond certain limit. On this basis of above examples we divide the flow of liquid in the following types,

(1) Streamline flow

• The flow of liquid in which all the layers of liquid are flows with constant velocities and the velocity of that individual layers is constant at all the points.
• Different layers of liquid appear like the parallel lines, known as stream. Hence this flow is also known as laminar flow.

(2) Turbulent flow

• The flow of liquid in which all the layers of liquid are flows with irregular/ different velocities called as turbulent flow.

When liquid flows in the form of streamlines, it follows certain conditions which give rise to equation of continuity.

Let’s derive equation of continuity……………!

Consider the liquid flowing through the pipe of different cross-sections as shown below.

Let A₁, A₂ and A₃ be the cross-sectional areas of pipe as shown in the fig. v₁, v₂ and v₃ be the velocities of liquid when flows from point A to B, C to D and E to F respectively.

Imagine that during the motion of liquid from points A to B, C to D and E to F it travels distance ∆x₁ , ∆x₂  and ∆x₃ in time ∆t.

Then the velocity of flow from point A to B is given by,

According to conservation of mass, the mass of liquid coming in is always equal to the mass of liquid going out. i.e. the mass of liquid during the flow through points A to B, C to D and E to F is ‘m’.

∴ mass of liquid from A to B=mass of liquid from C to D………..(2)

From the above equation we can conclude that the product of area and velocity in streamline flow is always constant. i.e. for streamline flow the area of flow of liquid is inversely proportional to the velocity of flow of liquid.

This is known of equation of continuity, which is applicable for streamline flow only.

Some important terms…..!

1. Velocity of liquid above which the streamlines becomes irregular and flow becomes irregular is known as critical velocity of flow.
2. Above critical velocity flow becomes irregular known as turbulent flow

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