When the left flow tube radius is increased, what happens to the flow rate?

When the left flow tube radius is increased, what happens to the flow rate?

• A. Flow rate decreases
• B. Flow rate remains the same
• C. Flow rate increases
• D. Flow becomes turbulent

Answer: (C)

Increasing the radius lowers the resistance to flow dramatically. In laminar flow through a long straight tube, Poiseuille’s law says the flow rate Q is proportional to r^4 when the pressure difference, fluid viscosity, and tube length are fixed. So when the left flow tube radius is increased, the resistance drops and the same pressure gradient pushes more fluid, causing the flow rate to increase. Turbulence isn’t guaranteed just by a larger radius; it depends on the Reynolds number, which also depends on velocity and density. But with the radius increase under a fixed driving pressure, the flow rate clearly goes up.

Increasing the radius lowers the resistance to flow dramatically. In laminar flow through a long straight tube, Poiseuille’s law says the flow rate Q is proportional to r^4 when the pressure difference, fluid viscosity, and tube length are fixed. So when the left flow tube radius is increased, the resistance drops and the same pressure gradient pushes more fluid, causing the flow rate to increase. Turbulence isn’t guaranteed just by a larger radius; it depends on the Reynolds number, which also depends on velocity and density. But with the radius increase under a fixed driving pressure, the flow rate clearly goes up.