A common parameter that can be used to predict turbulence in fluid flow is called the Reynolds number. The Reynolds number for fluid flow in a pipe is a dimensionless quantity defined as Re = ρυd/ηwhere ρ is the density of the fluid, υ is its speed, d is the inner diameter of the pipe, and η is the viscosity of the fluid. The criteria for the type of flow are as follows:• If Re < 2 300, the flow is laminar.• If 2 300 < Re < 4 000, the flow is in a transition region between laminar and turbulent.• If Re > 4 000, the flow is turbulent.(a) Let’s model blood of density 1.06 × 103 kg/m3 and viscosity 3.00 × 10–3 Pa · s as a pure liquid, that is, ignore the fact that it contains red blood cells. Suppose it is flowing in a large artery of radius 1.50 cm with a speed of 0.067 0 m/s. Show that the flow is laminar. (b) Imagine that the artery ends in a single capillary so that the radius of the artery reduces to a much smaller value. What is the radius of the capillary that would cause the flow to become turbulent? (c) Actual capillaries have radii of about 5–10 micrometers, much smaller than the value in part (b). Why doesn’t the flow in actual capillaries become turbulent?
Fluid Pressure
The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.
Gauge Pressure
Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.
A common parameter that can be used to predict turbulence in fluid flow is called the Reynolds number. The Reynolds number for fluid flow in a pipe is a dimensionless quantity defined as
Re = ρυd/η
where ρ is the density of the fluid, υ is its speed, d is the inner diameter of the pipe, and η is the viscosity of the fluid. The criteria for the type of flow are as follows:
• If Re < 2 300, the flow is laminar.
• If 2 300 < Re < 4 000, the flow is in a transition region between laminar and turbulent.
• If Re > 4 000, the flow is turbulent.
(a) Let’s model blood of density 1.06 × 103 kg/m3 and viscosity 3.00 × 10–3 Pa · s as a pure liquid, that is, ignore the fact that it contains red blood cells. Suppose it is flowing in a large artery of radius 1.50 cm with a speed of 0.067 0 m/s. Show that the flow is laminar. (b) Imagine that the artery ends in a single capillary so that the radius of the artery reduces to a much smaller value. What is the radius of the capillary that would cause the flow to become turbulent? (c) Actual capillaries have radii of about 5–10 micrometers, much smaller than the value in part (b). Why doesn’t the flow in actual capillaries become turbulent?
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
