ANS:D - Mach number is given by the ratio of the speed of the fluid to that of sound in the fluid under conditions of flow.

The correct statement among the options provided is: Mach number is given by the ratio of the speed of the fluid to that of sound in the fluid under conditions of flow. Here’s an explanation of each statement:

1. Fanning friction factor is inversely proportional to Reynolds number always.
   • This statement is incorrect. The Fanning friction factor fff is inversely proportional to the Reynolds number ReReRe for laminar flow, but for turbulent flow, it depends on the relative roughness of the pipe and Reynolds number. It does not hold true "always" across all flow regimes.
2. The property of a randomly packed bed (with Raschig rings) is given by the ratio of the total volume to the volume of voids in the bed.
   • This statement is incorrect. The property of a packed bed is typically characterized by parameters such as porosity (the ratio of void volume to total volume) or specific surface area, but it is not defined by the ratio of total volume to void volume.
3. Mach number in an incompressible fluid is always unity.
   • This statement is incorrect. Mach number (Ma) is defined as the ratio of the flow velocity to the speed of sound in the fluid. For incompressible fluids, where the speed of sound is infinitely high (since sound cannot propagate in them), the Mach number is effectively zero. It is not always unity; it depends on the flow conditions and fluid properties.
4. Mach number is given by the ratio of the speed of the fluid to that of sound in the fluid under conditions of flow.
   • This statement is correct. Mach number (Ma) is a dimensionless quantity that expresses the speed of an object moving through a medium (usually a fluid) relative to the speed of sound in that medium. It is given by Ma=VaMa = \frac{V}{a}Ma=aV​, where VVV is the velocity of the fluid and aaa is the speed of sound in the fluid.