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/m3, 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.
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?
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/m2.
Calculate the resistance of the hose.
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.
Fluid flows through a tube at a rate of cm3/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?
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 m2. 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?
What is the ratio of the retarding force from the air layer to the weight of the cart?
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.
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 garden hose with a radius of 0.900 cm, that is attached to a 0.250-cm-radius nozzle.