In frictional fluid flow, the quantity, , is

ANS:B - not constant along a streamline.

In frictional fluid flow, the quantity vμ\frac{v}{\mu}μv​, where vvv is the velocity of the fluid and μ\muμ is the dynamic viscosity of the fluid, is not constant along a streamline.

Explanation:

1. Dynamic Viscosity (μ\muμ): Dynamic viscosity is a measure of a fluid's resistance to flow under an applied force. It depends on the type of fluid and its temperature.
2. Velocity of the Fluid (vvv): Velocity varies along streamlines in frictional fluid flow, influenced by factors such as pressure gradients, flow obstacles, and boundary conditions.
3. Ratio vμ\frac{v}{\mu}μv​:
   • This ratio vμ\frac{v}{\mu}μv​ is significant because it represents the Reynolds number (ReReRe) for flow. Re=ρvLμRe = \frac{\rho v L}{\mu}Re=μρvL​, where ρ\rhoρ is the density of the fluid and LLL is a characteristic length.
   • ReReRe determines the flow regime (laminar or turbulent). For laminar flow, ReReRe is low, and vμ\frac{v}{\mu}μv​ is relatively constant along streamlines. In turbulent flow, ReReRe is high, and vμ\frac{v}{\mu}μv​ varies significantly.
4. Along a Streamline:
   • Along a streamline in frictional flow, velocity vvv may change due to pressure gradients or external forces, affecting vμ\frac{v}{\mu}μv​.
   • Therefore, vμ\frac{v}{\mu}μv​ is not constant along a streamline because velocity and thus vμ\frac{v}{\mu}μv​ can vary.
5. Conclusion:
   • vμ\frac{v}{\mu}μv​ is a critical parameter in fluid dynamics, influencing flow characteristics and Reynolds number calculations.
   • In summary, vμ\frac{v}{\mu}μv​ is not constant along a streamline in frictional fluid flow, reflecting the dynamic nature of fluid velocity and viscosity interactions.