Which law is used to describe pressure loss due to viscosity in laminar flow?

Which law is used to describe pressure loss due to viscosity in laminar flow?

• A. Continuity rule
• B. Bernoulli effect
• C. Poiseuille's law
• D. Reynolds number

Answer: (C)

In laminar flow through a long, straight pipe with a Newtonian fluid, the pressure drop is driven by viscous shear and is captured by Poiseuille's law. This law shows that the pressure difference needed to move a steady flow is proportional to the fluid’s viscosity, the pipe length, and the flow rate, and inversely proportional to the fourth power of the pipe radius. The standard form is ΔP = 8 μ L Q / (π r^4), with the inverse relation Q = π r^4 ΔP / (8 μ L). It relies on steady, incompressible, laminar flow in a circular cross-section and no-slip at the walls. While continuity, Bernoulli’s principle, and the Reynolds number are important in other contexts, Poiseuille’s law specifically describes how viscosity causes pressure loss in laminar pipe flow.

In laminar flow through a long, straight pipe with a Newtonian fluid, the pressure drop is driven by viscous shear and is captured by Poiseuille's law. This law shows that the pressure difference needed to move a steady flow is proportional to the fluid’s viscosity, the pipe length, and the flow rate, and inversely proportional to the fourth power of the pipe radius. The standard form is ΔP = 8 μ L Q / (π r^4), with the inverse relation Q = π r^4 ΔP / (8 μ L). It relies on steady, incompressible, laminar flow in a circular cross-section and no-slip at the walls. While continuity, Bernoulli’s principle, and the Reynolds number are important in other contexts, Poiseuille’s law specifically describes how viscosity causes pressure loss in laminar pipe flow.