Target GATE & ESE 2022 (Fluid Mechanics)

 Do you know?

👉Pressure gradient in the direction of flow (∂p/∂x) is equal to the shear gradient normal to the direction of flow (∂τ/∂y).

                                            ∂p/∂x  =   ∂τ/∂y        

👉 Hele Shaw Flow: Laminar flow between parallel plates

      Stoke's Law: Settling of fine particles

      Hagen Poiseuille Flow: Laminar flow in tubes/pipes

👉Bulk modulus(k) is a measure of compressibility of fluid. It is the ratio of change in pressure (△P) to change in volume per unit volume (∆V/V). It is also called ratio of pressure to volumetric strain.

👉 Various factors that affect bulk modulus:

    > As pressure of fluid increases, bulk modulus of elasticity of fluid increases.

    > With increase in temperature of a liquid the bulk modulus of liquid decreases.

    > With increase in temperature of a gas the bulk modulus of gas increases

.👉Streak line is formed by continuous introduction of dye or smoke from a pont in the flow.

👉 For steady flow ⟶ Stream line, Path line and Streak line are same.

👉Cauchy-Riemann Equation 

> Velocity potential function exists only for irrotational flow.

> Stream function exists both for rotational & irrotational flow.

> Both velocity potential and stream function for irrotational flow satisfies laplace equation.

> For irrotational incompressible flow 

               u = -∂Φ/∂x = -∂Ψ /∂y

               v = -∂Φ/∂y = ∂Ψ /∂x

👉Flow Net

◘ A line along which stream function is constant is called stream line (ψ = Constant)

◘ A line along which velocity potential is constant is called equipotential line ( Φ = constant)

◘ A grid obtained by drawing series of equipotential lines and stream lines is known as flow net.

◘Flow net is drawn in such a way that difference between stream function stream function of two successive stream lines are same. Discharge between two successive stream line is constant in a flow net.

 

👉 Methods of drawing Flow Net

◘  Analytical method

◘  Hydraulic models

◘ Graphical method

◘ Electrical analogy method

👉 Use of Flow Net

◘  Determine uplift pressure on the bottom of a dam

◘  Loss of flow due to seepage in earth dam  

◘  Determine the stream line and equipotential lines.

    

                                                    Happy Learning