Question

In: Civil Engineering

question 1 : A velocity potential in a two-dimensional flow is given as φ = 3xy2...

question 1 :

A velocity potential in a two-dimensional flow is given as φ = 3xy2 – x3 . Find the stream function which is perpendicular to velocity potential

question 2 :

Write down equations that represents the volume flow rate and the mass flow rate. Show the resultant units of equations in terms of MLT system

Expert Solution

We know that

Velocity component in x-direction is given by

= - 3y² + 3x²

Velocity component i y -direction is given by

= - 6xy

Also Stream function is given by

Integrating both sides

= -3x²y + C ......(1)

where C = constant of integration

Also

Integrate b/s

C = y³

Put in(1)

2.) Volume flow rate(Q) is given by

Q = AxV

where V = velocity in m/s

A = area in m²/s

Units of volume flow rate is m³/s in SI system i.e [M⁰L³T^-1]

Mass flow rate (m) is given by

where = density of fluid

Units of mass flow rate is kg/sec in SI system i.e [ML^oT^-1]

Ally Wells answered 1 year ago

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