Q1: Which of the following must be followed by the flow of a fluid (real or ideal)?
(I) Newton's law of viscosity.
(II) Newton's second law of motion.
(III) The continuity equation.
(IV) Velocity of boundary layer must be zero relative to boundary.
(V) Fluid cannot penetrate a boundary.

ANS:B - II, III, V

To determine which statements must be followed by the flow of a fluid (real or ideal), let's analyze each option:

1. Newton's law of viscosity (I): This law states that the shear stress τ\tauτ between adjacent fluid layers is directly proportional to the velocity gradient dudy\frac{du}{dy}dydu​ perpendicular to the direction of flow. This is a fundamental principle governing the behavior of viscous fluids, so it must be followed.
2. Newton's second law of motion (II): This law states that the rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the applied force. For fluids, this law is applicable in the context of fluid dynamics, where forces such as pressure gradients and gravitational forces influence fluid motion. Therefore, it must also be followed.
3. The continuity equation (III): The continuity equation expresses the principle of conservation of mass for a fluid flow. It states that the mass flow rate is constant along a streamline and is given by ρAV=constant\rho A V = \text{constant}ρAV=constant, where ρ\rhoρ is the density, AAA is the cross-sectional area, and VVV is the velocity. This equation is a fundamental law in fluid dynamics and must be satisfied.
4. Velocity of boundary layer must be zero relative to boundary (IV): This statement is incorrect. In fluid dynamics, the boundary layer is the thin layer of fluid near the surface where viscous effects are significant. The velocity of the boundary layer relative to the boundary (surface) is not zero; rather, it varies smoothly from zero at the surface to the free stream velocity away from the surface. Therefore, this statement does not need to be followed.
5. Fluid cannot penetrate a boundary (V): This statement is generally true. A boundary typically separates different regions or phases of a system, and fluids generally do not penetrate solid boundaries. Instead, they flow around or along boundaries depending on the flow conditions and boundary shape. Thus, this statement must be followed.

• Statements I, II, and V are correct and must be followed by the flow of a fluid (real or ideal).
• Therefore, the correct answer is I, II, V.