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In a twodimensional flow, the velocity components in x and y directions in terms of stream function (ψ) are
For stream function:
Velocity component in xdirection
Velocity component in ydirection
If φ is the velocity potential function in 2D flow field, then the velocity components u and v are defined as
For velocity potential function
Velocity component in x direction
Velocity component in ydirection
The convective acceleration of fluid in the xdirection is given by
Stream line is an imaginary line drawn in space such that a tangent drawn to it at any point gives velocity at that point.
A steady incompressible flow is given by
Q. What is the convective acceleration along xdirection at point (1, 2)?
Convective acceleration along x direction
for 2D flow (w=0)
a_{x} = (2x^{2} + y^{2})(4x)  4xy(2y)
ax = 8x^{3} + 4xy^{2}  8xy^{2}
at (12)
a_{x} = 8 + 16  32 =  8 unit
Match ListI with Listll and select the correct answer using the codes given below the lists:
ListI
A. Stream line
B. Streak line
C. Path line
D. Equipotential lines
ListII
1. Tracing of motion of any fluid particle
2. Tracing of motion of different fluid particles
3. Identification of location of number of fluid particles
4. Orthogonal to streak lines
5. Location of equal piezometric head
Codes:
A B C D
(a) 2 3 4 5
(b) 3 2 1 4
(c) 1 2 4 3
(d) 2 3 1 5
Stream Line — Curves drawn tangential to the velocity vector at all points in the flow field at any instance of time. They represent Eulerian approach for flow field.
Streak Line — It is locus of the temporary location of all the particles that have passed through a fixed point in the flow field.
The stream function for a twodimensional flow is given by ψ = 2xy. The velocity at (2, 2) is
Resultant =
You are asked to evaluate assorted fluid flows for their suitability in a given laboratory application. The following three flow choices, expressed in terms of 2D velocity field in the xy plane, are made available
P. u = 2y,v = 3x
Q. u = 3xy, v = 0
R. u = 2x , v = 2 y
Which flow(s) should be recommended when the application requires the flow to be incompressible and irrotational
The continuity equation in differential form is
Continuity equation
ρAV = constant
By differentiating the equation
Av.dρ + ρvdA + ρAdV = 0
By dividing pAv, we get
Given φ = 3 xy and ψ = 3/2(y^{2}  x^{2}) , the discharge passing between the stream tines through the point (1,3) and (3,3) is
Note that difference between two stream line is discharge per unit width
If the stream function is given by ψ = 3xy then the velocity at a point (2,3) will be
Resultant
An open circular cylinder 1.2 m height is filled with a liquid to its top. The liquid is given a rigid body rotation about the axis of the cylinder and the pressure at the centre line at the bottom surface is found to be 0.6 m of liquid. What is the ratio of volume of liquid spilled out of the cylinder to the original volume
original volume of cylinder = πr^{2}h
volume of liquid spilled out = 1/2 πr^{2}h
In a two dimensional velocity field with velocities u and v along the x and y directions respectively the convective acceleration along the xdirection is given by
A type of flow in which the fluid particle while moving in the direction of flow rotates about their centre is known as
For the continuity equation given by to be valid, where is the velocity vector, which one of the following is a necessary condition?
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