Fluid Mechanics and Hydraulic Machinery Miscellaneous
 If the fluid velocity for a potential flow is given by V(x, y) = u(x, y)i + v(x, y)j with usual notations, then the slope of the potential line at (x, y) is

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Here V(x, y) = u(x, y) i + v(x, y) j
As we know that u = δφ δx ∴ δφ = v(x,y) ....(i) δx Similarly v = δφ δy ∴ δφ = v(x,y) ....(ii) δy
From equations (i) and (ii) we get,
Correct Option: B
Here V(x, y) = u(x, y) i + v(x, y) j
As we know that u = δφ δx ∴ δφ = v(x,y) ....(i) δx Similarly v = δφ δy ∴ δφ = v(x,y) ....(ii) δy
From equations (i) and (ii) we get,
 Consider a velocity field V K(yi + xk), where K is a constant. The vorticity, Ω Z, is

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NA
Correct Option: A
NA
 Consider the following statements regarding streamline(s):
(i) It is a continuous line such that the tangent at any point on it shows the velocity vector at that point
(ii) There is no flow across streamlines
(iii)dx = dy = dz is the differential equation of a streamline, where u, v and w are velocities in directions x, y and z, respectively u v w
(iv) In an unsteady flow, the path of a particle is a streamline
Which one of the following combinations of the statements is true?

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NA
Correct Option: D
NA
 A cube of side 100 mm is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is 800 kg/m^{3}. Liquid of densit y 1000 k g/m^{3} is now poured into the container. The minimum height to which the liquid needs to be poured into the container for the cube to just lift up is _____ mm.

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Given, side of cube (a) = 100 m
Density of material of cube = 800 kg/m^{3}
Poured liquid density = 1000 kg/m^{3}
Now, Minimum height to which the liquid needs to be poured into the container for the cube to just lift up, should satisfy the condition
F_{B} ≥ (mg)_{block}
ρ_{f}gV_{fd} ≥ (ρV)_{block}× g
1000 × 0.1 × h ≥ 800 × 0.1 × 0.1 × 0.1
h ≥ 0.08 m
h ≥ 80 mCorrect Option: A
Given, side of cube (a) = 100 m
Density of material of cube = 800 kg/m^{3}
Poured liquid density = 1000 kg/m^{3}
Now, Minimum height to which the liquid needs to be poured into the container for the cube to just lift up, should satisfy the condition
F_{B} ≥ (mg)_{block}
ρ_{f}gV_{fd} ≥ (ρV)_{block}× g
1000 × 0.1 × h ≥ 800 × 0.1 × 0.1 × 0.1
h ≥ 0.08 m
h ≥ 80 m
 For the stability of a floating body the

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NA
Correct Option: D
NA