Which law describes laminar flow in a long straight tube?

Which law describes laminar flow in a long straight tube?

• A. Bernoulli's law
• B. Poiseuille's law
• C. Reynolds number
• D. Doppler equation

Answer: (B)

Poiseuille's law describes how laminar, pressure-driven flow behaves in a long straight tube. It shows that the volumetric flow rate is determined by the pressure difference driving the flow, the tube’s radius, the fluid’s viscosity, and the tube length. Specifically, for steady, incompressible, Newtonian fluid with no-slip walls, the flow rate scales with the radius to the fourth power and with the pressure difference, while it is reduced by higher viscosity and longer tubes. The practical upshot is that doubling the radius makes a huge difference in how much fluid can pass through, whereas thicker tubes slow the flow and longer tubes require a larger pressure drop to push the same amount of fluid. Other concepts don’t describe this direct relationship. Bernoulli’s law deals with energy conservation along a streamline and doesn’t give a formula for flow rate in terms of pressure drop. Reynolds number tells you whether the flow is likely to be laminar or turbulent but isn’t the equation governing the actual flow rate. The Doppler equation relates observed frequency shifts due to motion, not fluid transport in pipes.

Poiseuille's law describes how laminar, pressure-driven flow behaves in a long straight tube. It shows that the volumetric flow rate is determined by the pressure difference driving the flow, the tube’s radius, the fluid’s viscosity, and the tube length. Specifically, for steady, incompressible, Newtonian fluid with no-slip walls, the flow rate scales with the radius to the fourth power and with the pressure difference, while it is reduced by higher viscosity and longer tubes. The practical upshot is that doubling the radius makes a huge difference in how much fluid can pass through, whereas thicker tubes slow the flow and longer tubes require a larger pressure drop to push the same amount of fluid.

Other concepts don’t describe this direct relationship. Bernoulli’s law deals with energy conservation along a streamline and doesn’t give a formula for flow rate in terms of pressure drop. Reynolds number tells you whether the flow is likely to be laminar or turbulent but isn’t the equation governing the actual flow rate. The Doppler equation relates observed frequency shifts due to motion, not fluid transport in pipes.