JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year CHEMICAL ENGINEERING FLUID MECHANICS Previous Question Paper (April/May - 2023 - R13)

Dimensionally non-homogeneous equations are those in which the dimensions of each term on both sides of the equation are not identical. In such equations, the numerical coefficients depend on the system of units used, meaning the equation is not physically consistent across different unit systems.

An example is the empirical formula for the velocity of flow in a pipe, such as the Hazen-Williams equation or simple empirical relations like

When a fluid flows in bulk past a solid boundary, a velocity field develops primarily due to the no-slip condition, which dictates that fluid particles in direct contact with the solid surface must have the same velocity as the surface (zero relative velocity). This creates a velocity gradient perpendicular to the wall, resulting in the following phenomena:

• Viscous Shear Forces: The difference in velocity between adjacent fluid layers generates internal friction, known as shear stress, which acts to retard the motion of fluid layers near the wall.
• Boundary Layer Formation: This retardation effect propagates into the bulk fluid, leading to the development of a thin region called the boundary layer, where viscous effects are significant and velocity increases from zero at the wall to the free-stream velocity.
• Momentum Transfer: The velocity field is established as momentum is transferred from the high-velocity bulk fluid toward the slower fluid layers near the solid surface through molecular diffusion and, in turbulent flow, through eddy transport.