# 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?

**Q3: **

A small artery has a length of m and a radius of m. If the pressure drop across the artery is 1.3 kPa, what is the flow rate through the artery if the viscosity of the blood is 2.084 Pa⋅s?

- A
mm
^{3}/s - B
mm
^{3}/s - C
mm
^{3}/s - D
mm
^{3}/s - E
mm
^{3}/s

**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

**Q6: **

At what flow rate might turbulence begin to develop in a water main with a 0.200 m diameter? Use a value of Pa⋅s for the viscosity of water and assume that a Reynolds number of corresponds to the onset of turbulence.

- A
m
^{3}/s - B
m
^{3}/s - C
m
^{3}/s - D
m
^{3}/s - E
m
^{3}/s

**Q7: **

Calculate the Reynolds numbers for the flow of water through the following objects if the flow rate is 0.500 L/s.

A nozzle with a radius of 0.250 cm.

- A
- B
- C
- D
- E

A garden hose with a radius of 0.900 cm, that is attached to a 0.250-cm-radius nozzle.

- A
- B
- C
- D
- E

**Q8: **

Calculate the Reynolds number for water flowing through a 1-inch-radius pipe at a flow rate of 0.631 L/s. Use a value of Pa⋅s for the dynamic viscosity of water.

**Q9: **

A plate flow reaches Reynolds number of . Which type of flow is it?

- ATransition between turbulent and laminar
- BTurbulent
- CThe fluid is at rest
- DLaminar
- ECyclical flow

**Q10: **

The viscosity of a dilute inert gas at a temperature of 100 K is 20 μPa⋅s and at a temperature of 500 K is 45 μPa⋅s. What is the viscosity of the gas at a temperature of 300 K?

**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?

**Q12: **

The density of an unknown fluid is 0.78 g/mL. A 2-millimeter-diameter brass ballbearing takes 2.8 s to fall 25 cm through the fluid. What is the fluid’s viscosity?

**Q13: **

For laminar flow of a Newtonian fluid in a circular pipe, what is the ratio of the peak fluid velocity to the cross-sectional average velocity?

**Q14: **

For fully turbulent flow of a Newtonian fluid in a circular pipe of radius , the fluid’s velocity profile can be well–approximated by , with . What is the ratio of the peak fluid velocity to the cross-sectional average velocity?

**Q15: **

An oil flows with a mass flow rate of 14.17 L/s through a pipe of diameter of 15.00 cm.
The viscosity and density of the oil are 0.1041 Pa⋅s and 917 kg/m^{3} respectively. What is the pressure drop per meter in the pipe?

**Q16: **

The pressure drop in a flow of oil in a smooth and straight pipe of diameter 5.00 cm is kPa/m. Find the oil’s flow rate. Use a value of 0.90 for the specific gravity of oil and use a value of 0.10 kg/m⋅s for the oil’s viscosity.

**Q17: **

Air flows over a sharp flat plate at a speed of 2.5 m/s.
Calculate the thickness of the boundary layer of air
50 cm
away from the plate edge.
Use a value of
1.2 kg/m^{3}
for the air’s density and use a value of
m^{2}/s
for the air’s kinematic viscosity.

**Q18: **

The absolute viscosity of an oil is 0.100 kg/m⋅s and its specific gravity is 0.800. Calculate the kinematic viscosity of the oil.

- A
m
^{2}/s - B
m
^{2}/s - C
m
^{2}/s - D
m
^{2}/s - E
m
^{2}/s

**Q19: **

Glycerin with a density of
kg/m^{3}
and a viscosity of
0.96 Pa⋅s
flows in a pipe with a diameter of
15.0 cm.
What is the characteristic of the flow if its speed is
4.0 m/s?

- Aboth turbulent and laminar
- BSupersonic
- CTurbulent
- DLaminar
- EDissipative

**Q20: **

Water with a density of 998 kg/m^{3} and a viscosity of N⋅s/m^{2}
flows through a straight smooth pipe with a diameter
of 1.00 cm. What is the speed of the
flow at which transition to turbulence occurs?

**Q21: **

What does the Reynolds number measure?

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

**Q22: **

Transition from a laminar pipe flow to a turbulent flow typically occurs with a Reynolds number in what range?

- A10
^{5}-10^{6} - B500–1 000
- C50 000–100 000
- D2 000–4 000
- E25–50

**Q23: **

What dimensionless number is used to compare surface tension with inertial forces in fluid flows?

- APrandtl number
- BReynolds number
- CFroude number
- DWeber number
- EEuler number