Stream Function

Q. For a 2-D flow field, the stream function $\psi$ is given as $\psi =\frac{3}{2}(y^2-x^2)$.
The magnitude of discharge occurring between the stream line passing through points (0, 3) and (3, 4) is

1. 6 units
2. 3 units
3. 1.5 units
4. 2 units

Q. If the stream function $\psi =3x^2-y^3$, what is the magnitude of velocity at point (2, 2)?

1. 9
2. 13
3. 15
4. 17

Q. Given $\varphi =3xyand\psi =\frac{3}{2}(y^2-x^2)$, the discharge passing between the streamlines through the points (1, 3) and (3, 3)

1. 2 units
2. 4 units
3. 8 units
4. 12 units

Q. Consider the following parameters related to fluid flow:

1. Vorticity
2. Velocity potential
3. Stream function
Among these, those which exist both in rotational flows and irrotational flows should include

1. 1 and 2
2. 2 and 3
3. 1 and 3
4. 1, 2 and 3

Q. In a parallel two-dimension flow in the positive x-direction, the velocity varies linearly from zero at y = 0 to 75 m/sec at y = 1m. The expression for $\psi$ is given by

1. $22.5y^2$

2. $30.0y^2$

3. $37.5y^2$
4. $45.0y^2$

Q. A two-dimensional flow is described by velocity components
u = 2x and v= -2y. The discharge between points (1, 1) and (2, 2) is equal to

1. 9 units
2. 8 units
3. 7 units
4. 6 units

Q. For stream function $\psi =3x^2-y^3$, the magnitude of velocity at the point (2, 1) is

1. 12.37
2. 12
3. 13
4. 13.5

Q. In a two-dimensional flow, with its stream function $\psi =2xy$, the velocity at a point (3, 4) is

1. 12.0 units
2. 10.0 units
3. 8.0 units
4. 6.0 units

Q. The stream function for a two-dimensional flow is given by $\psi =2xy$. The resultant velocity at a point P(2, 3) is

1. 8.45 units/s
2. 7.21 units/s
3. 6.44 units/s
4. 5.18 units/s

Q. The volumetric flow rate (per unit depth) between two streamlines having stream function ${\Psi }_{1}and{\Psi }_2$ is

1. $|{\Psi }_1+{\Psi }_2|$
2. ${\Psi }_1{\Psi }_2$
3. ${\Psi }_1/{\Psi }_2$
4. $|{\Psi }_1-{\Psi }_2|$