The ratio of inertial forces to viscous forces is called the __________ number.

ANS:D - Reynold

The ratio of inertial forces to viscous forces is called the Reynolds number. Here’s an explanation:

1. Definition: The Reynolds number (Re) is a dimensionless quantity used in fluid mechanics to predict flow patterns in different fluid flow situations. It is defined as: Re=ρVLμ\text{Re} = \frac{\rho V L}{\mu}Re=μρVL​ where:
   • ρ\rhoρ is the density of the fluid,
   • VVV is the characteristic velocity of the flow,
   • LLL is a characteristic length (such as diameter for pipe flow),
   • μ\muμ is the dynamic viscosity of the fluid.
2. Significance: The Reynolds number indicates the relative importance of inertial forces (due to the fluid's momentum) to viscous forces (resistance to flow due to fluid viscosity). It determines whether flow is laminar, turbulent, or in a transitional state between these two regimes.
3. Flow Regimes:
   • Laminar Flow (Re < 2000): In this regime, viscous forces dominate, and flow is smooth and orderly with well-defined streamlines.
   • Turbulent Flow (Re > 4000): Here, inertial forces dominate, and flow is chaotic with irregular fluctuations in velocity and pressure.
   • Transitional Flow (2000 < Re < 4000): Flow characteristics are between laminar and turbulent, with intermittent turbulence and varying flow patterns.
4. Applications: The Reynolds number is fundamental in fluid dynamics and has applications in various fields such as engineering (design of pipes, aircraft, and vehicles), biology (blood flow in arteries), meteorology (atmospheric flows), and more.