Consider the following statements related to concept of continuity equation and the concept of control volume in deriving the equation.
1. Continuity equation relates velocity component and density of the fluid at a point in a fluid flow.
2. Continuity equation assumes that no void occurs in the fluid and fluid mass is neither created nor destroyed.
3. The shape of control volume for deriving the equation of continuity is assumed to be a parallelepiped.
4. For incompressible fluids the equation of continuity does not contain the viscosity terms.

Which of these statements are correct?

1, 2, 3 and 4

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1 and 2

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2, 3 and 4

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1 and 4

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Solution

The correct option is A 1, 2, 3 and 4
(a)
Continuity equation is mathematical form of principle of conservation of mass. It also assumes the continuum of fluid i.e. there are no air voids in the fluid.

The continuity equation from control volume approach is
$\frac{\partial}{\partial t} \iint C V ρ d V + \iint C S ρ . \to V . d \to A = 0 [I n t e g r a l f o r m]$

where

dV is volume of differential element
CV is control volume
CS is control surface

$\frac{\partial ρ}{\partial t} + \to \nabla . (ρ \to V) = C [D i f f e r e n t i a l f o r m]$

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