12.5 The Onset of Turbulence

Verify that the flow of oil is laminar (barely) for an oil gusher that shoots crude oil 25.0 m into the air through a pipe with a 0.100-m diameter. The vertical pipe is 50 m long. Take the density of the oil to be $\text{900 kg} /\text{m}^{3}$ and its viscosity to be $1.00 \left(\right. \text{N}/\text{m}^{2} \left.\right) \cdot \text{s}$ (or $1.00 Pa \cdot \text{s}$).

Calculate the Reynolds numbers for the flow of water through (a) a nozzle with a radius of 0.250 cm and (b) a garden hose with a radius of 0.900 cm, when the nozzle is attached to the hose. The flow rate through hose and nozzle is 0.500 L/s. Can the flow in either possibly be laminar?

Concrete is pumped from a cement mixer to the place it is being laid, instead of being carried in wheelbarrows. The flow rate is 200.0 L/min through a 50.0-m-long, 8.00-cm-diameter hose, and the pressure at the pump is $8 . \text{00} \times \text{10}^{6} \text{N}/\text{m}^{2}$. Verify that the flow of concrete is laminar taking concrete’s viscosity to be $48.0 \left(\text{N}/ \text{m}^{2}\right) \cdot \text{s}$, and given its density is $2300 kg/ \text{m}^{3}$.

What is the greatest speed of blood flow at $\text{37}º\text{ C}$ in an artery of radius 2.00 mm if the flow is to remain laminar? What is the corresponding flow rate? Take the density of blood to be $1025 kg / \text{m}^{3}$.

Gasoline is piped underground from refineries to major users. The flow rate is $3 . \text{00} \times \text{10}^{–2} \text{m}^{3} /\text{s}$ (about 500 gal/min), the viscosity of gasoline is $1.00 \times \text{10}^{–3} \left(\right. \text{N}/\text{m}^{2} \left.\right) \cdot \text{s}$, and its density is $\text{680} \text{kg}/\text{m}^{3}$. (a) What minimum diameter must the pipe have if the Reynolds number is to be less than 2000? (b) What pressure difference must be maintained along each kilometer of the pipe to maintain this flow rate?

A fairly large garden hose has an internal radius of 0.600 cm and a length of 23.0 m. The nozzleless horizontal hose is attached to a faucet, and it delivers 50.0 L/s. (a) What water pressure is supplied by the faucet? (b) What is unreasonable about this pressure? (c) What is unreasonable about the premise? (d) What is the Reynolds number for the given flow? (Take the viscosity of water as $1.005 \times 10^{–3} \left(\text{N} / m^{2}\right) \cdot \text{s}$.)