# Worksheet: Viscosity and Turbulence

In this worksheet, we will practice using Poiseuille's law for laminar fluid flow and modeling the onset of turbulence with Reynolds numbers.

**Q1: **

Stokes’ law describes sedimentation of particles in
liquids and can be used to measure viscosity. Particles in
liquids achieve terminal velocity quickly. One can measure
the time it takes for a particle to fall a certain distance and
then use Stokes’ law to calculate the viscosity of the liquid.
Suppose a steel ball bearing (density kg/m^{3},
diameter 3.0 mm) is dropped in a container of motor oil.
It takes 12 s to fall a distance of 0.60 m. Calculate the
viscosity of the oil.

**Q2: **

Fluid flows through a tube at a rate of
cm^{3}/s.

The pressure difference across the tube increases by a factor of 1.50. What is the flow rate through the tube if no other changes are made?

A fluid with a viscosity 3.00 times greater than that of the original fluid flows through the tube. What is the flow rate through the tube if no other changes are made?

The length of the tube is increased by a factor of 4.00. What is the flow rate through the tube if no other changes are made?

The radius of the tube is reduced by a factor of 10.0. What is the flow rate through the tube if no other changes are made?

The radius of the tube is reduced by a factor of 10.0. The length of the tube is reduced by a factor of 2.00, and the pressure difference across the tube is increased by a factor of 1.50. What is the flow rate through the tube if no other changes are made?

**Q4: **

Concrete is pumped from a cement mixer to the place
it is being laid, instead of being carried in wheelbarrows.
The flow rate is 200 L/min through a 50.0-m-long,
8.00-cm-diameter hose, and the pressure at the pump is N/m^{2}.

Calculate the resistance of the hose.

- A
N⋅s/m
^{5} - B
N⋅s/m
^{5} - C
N⋅s/m
^{5} - D
N⋅s/m
^{5} - E
N⋅s/m
^{5}

What is the viscosity of the concrete, assuming the flow is laminar?

How much power is being supplied, assuming the point of use is at the same level as the pump? You may neglect the power supplied to increase the concrete’s velocity.

- A W
- B W
- C W
- D W
- E W

**Q5: **

A cart of mass 0.300 kg moves horizontally at 0.400 m/s, generating some resistance from a layer of air passing over its surface. The surface area of the cart in contact with the air is m^{2}. The thickness of the layer of air is m and the air’s viscosity is 0.0181 Pa⋅s.

What is the retarding force of the air layer on the cart?

- A N
- B N
- C N
- D N
- E N

What is the ratio of the retarding force from the air layer to the weight of the cart?

- A
- B
- C
- D
- E

**Q11: **

A flat steel plate of
5.00 mm thickness,
1.00 m length,
and
0.500 m width is falling through
the atmosphere with its 1.00-meter-length side aligned vertically.
The density of the steel is
kg/m^{3}.
The air in the region of the plate has a density of
1.20 kg/m^{3},
a thermal conductivity of
0.0260 W/m⋅K,
and a viscosity of
m^{2}/s.
What is the terminal velocity of the plate?

**Q21: **

What does the Reynolds number measure?

- AThe ratio of gravitational force to fluid’s inertia.
- BThe ratio of a fluid's flow rate to the pressure it exerts.
- CThe ratio of momentum diffusivity to thermal diffusivity.
- DThe ratio of surface tension to inertial forces.
- EThe ratio of inertial forces V
^{2}/L to viscous forces V/L^{2}.