Water flows at a speed of 6 cm s^-1 through a tube of radius 1 cm. Coefficient of viscosity of water at room temperature is 0.01 poise. Calculate the Reynolds number. It a steady flow?

A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plot shown in Fig. 10.1, indicate the one that represents the velocity (v) of the pebble as a function of time (t).

Is viscosity a vector?

Water flows at a speed of 6 cm s^-1 through a tube of radius 1 cm. Coefficient of viscosity of water at room temperature is 0.01 poise. Calculate the Reynolds number. It a steady flow?

A metal sphere of radius 1 mm and mass 50 mg falls vertically in glycerin. Find (a) the viscous force exerted by the glycerin on the sphere when the speed of the sphere is 1 cm s’, (b) the hydrostatic force exerted by the glycerin on the sphere and (c) the terminal velocity with which the sphere will move down without acceleration. Density of glycerin = 1260 kg m^-3 and its co-efficient of viscosity at room temperature = 8.0 poise.

Estimate the speed of vertically falling raindrops from the following data. Radius of the drops 0.02 cm, viscosity of air = 1.8 × 10-⁴ poise, g = 9.9 × 10 m s^-2 and density of water = 1000 kg m^-3.

What is the largest average velocity of blood flow in an artery of radius 2 × 10^–3m if the flow must remain lanimar?

What is the corresponding flow rate? (Take viscosity of blood to be 2.084 × 10^–3 Pa s).

In Millikan’s oil drop experiment, what is the terminal speed of an uncharged drop of radius 2.0 × 10^–5 m and density 1.2 × 10³ kg m^–3. Take the viscosity of air at the temperature of the experiment to be 1.8 × 10^–5 Pa s. How much is the viscous force on the drop at that speed? Neglect buoyancy of the drop due to air.

Glycerine flows steadily through a horizontal tube of length 1.5 m and radius 1.0 cm. If the amount of glycerine collected per second at one end is 4.0 × 10^–3 kg s^–1, what is the pressure difference between the two ends of the tube? (Density of glycerine = 1.3 × 10³ kg m^–3 and viscosity of glycerine = 0.83 Pa s). [You may also like to check if the assumption of laminar flow in the tube is correct].

In deriving Bernoulli’s equation, we equated the work done on the fluid in the tube to its change in the potential and kinetic energy. (a) What is the largest average velocity of blood flow in an artery of diameter 2 × 10^–3 m if the flow must remain laminar? (b) Do the dissipative forces become more important as the fluid velocity increases? Discuss qualitatively.