Sticky flow, narrow pipes, rough flow

Science · Forces & Motion · ages 20-21

Name ______________________ Date ____________

Which quantities are needed to calculate the diameter-based Reynolds number for pipe flow?
- Fluid density, mean speed, pipe diameter and dynamic viscosity
- Pressure difference, tube length, pipe diameter and fluid temperature
- Fluid mass, pipe volume, mean speed and gravitational field strength
A horizontal circular tube obeys Poiseuille's law before and after its radius is halved. Pressure difference, tube length and viscosity stay fixed. By what factor is the volume flow rate reduced?
- 2
- 4
- 16
An incompressible Newtonian fluid has steady, fully developed, pressure-driven laminar flow in a straight, uniform circular tube with stationary, no-slip walls. The fluid moves fastest at the walls. True or false?
Circle one: True False
Ordinary flow in a straight circular pipe has a diameter-based Reynolds number of 20000. What is the usual expectation?
- Laminar flow with all disturbances damped away
- Turbulent flow with eddies and cross-stream mixing
- Stopped flow with no fluid passing through the pipe
A horizontal circular tube carries 3 mL/s. Its radius doubles while pressure difference, tube length and viscosity stay fixed. Assume Poiseuille's law applies before and after the change. What is the new volume flow rate in mL/s?
Answer: ______________
Which situation meets the assumptions of the usual Bernoulli equation between two points?
- Steady incompressible flow along a streamline, with negligible losses and no pump or turbine
- Steady incompressible flow along a streamline, with large viscous losses in a long narrow tube
- Steady compressible flow along a streamline, with large density changes between the chosen points
A fluid has density 1000 kg/m³, mean pipe speed 1 m/s, pipe diameter 0.01 m and dynamic viscosity 0.01 Pa s. What is its diameter-based Reynolds number?
Answer: ______________
Honey flows steadily through a long narrow tube with a large viscous pressure loss. Mira says, 'Its Reynolds number is low, so I can ignore that loss in Bernoulli's equation.' Which reply fits?
- Low Re makes the honey frictionless, so the Bernoulli sum stays constant
- Low Re favours laminar flow, but viscous losses can still be large
- Low Re removes the pressure drop, so pressure is equal at both tube ends

Answer key

For grown-ups. Fold this page away before handing over the rest.

Sticky flow, narrow pipes, rough flow W1-mt_-1sWgkRtMs-s1

Fluid density, mean speed, pipe diameter and dynamic viscosity · Use Re = rho*v*D/mu. Here rho is fluid density, v is mean speed, D is pipe diameter and mu is dynamic viscosity.
16 · The radius factor is 1/2, so the flow factor is (1/2)^4 = 1/16. The flow rate is reduced by a factor of 16.
False · No slip makes the fluid speed zero at each stationary wall. The parabolic profile reaches its maximum at the centre.
Turbulent flow with eddies and cross-stream mixing · 20000 is well above the pipe transition range of a few thousand, so turbulence is usually expected. Reynolds number is an indicator, not a universal guarantee.
48 · Doubling radius multiplies Poiseuille flow by 2^4 = 16. The new flow rate is 3*16 = 48 mL/s.
Steady incompressible flow along a streamline, with negligible losses and no pump or turbine · The usual Bernoulli equation needs steady, incompressible flow with negligible losses along the chosen streamline and no pump or turbine between the points.
1000 · Re = rho*v*D/mu = (1000*1*0.01)/0.01 = 1000. These SI units give a dimensionless result.
Low Re favours laminar flow, but viscous losses can still be large · Low Reynolds number does not mean negligible dissipation. The stated large viscous loss must appear in the energy balance; total energy is still conserved.