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Mechanical Properties of Fluids
Question
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Horizontal tube of non-uniform cross-section has radii of 0.1 m and 0.05 m respectively at M and N. For a streamline flow of liquid, the rate of liquid flow is

              

  • changing continuously with time

  • greater at M than at N

  • greater at N than at M

  • same at M and N

Answer

C.

greater at N than at M

The mass flow per unit time passing through each cross-section does not change, even if the pipe diameter changes. This is the law of conservation of mass.

A continuity equation in physics is an equation that describes the transport of some quantity. It is perticularly simple and powerful when applied to conserved quantity. 

According to the equation of continuity

            ρ A v  = constant

 If the fluid is incompressible e.g water, with ρ being effectively constant, then

             A v = constant

Where A is the area of cross-section, v is the velocity and ρ is the density of a fluid.

Av gives the volume flux or flow rate remains constant throughout the pipe of flow.      

The velocity of flow will increase if cross-section decreases and vice-versa.

 

i.e                         A1 V1 = A2 V2

⇒                            Av = constant

Therefore, the rate of liquid flow will be greater at N than at M.

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