3.3 Newtonian Fluid Fluid such as water , air, ethanol and benzene are Newtonian. The shear stress is plotted against shear rate at a given temperature; the figure ( 6 ) shows a straight line with a constant slope that is independent of shear rate. This slope is called the viscosity of the fluid. The simplest constitutive equation is Newton‟s law of viscosity; ...................( ) where μ = the Newtonian viscosity and γ = shear rate or the rate of strain.
The Newtonian fluid is the basis for classic fluid mechanics [Munson et al., 1998]. Gases and liquids like water and mineral oils exhibit characteristics of Newtonian viscosity. Blood is often assumed to be Newtonian fluid for modeling purposes. In
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Hence, the value of n determines the classes of the fluid which is as follow: n = 1 (Newtonian Fluid) n > 1 shear-thickening (Dilatant fluids) n < 1 shear-thinning (pseudo-plastics)
These three types of power-law models are clarified butter in Figure. 2-2.
Unfortunately, one of the evident disadvantages of the power-law model is that it fails to portray the viscosity of many non-Newtonian fluids in very low shear rate regions and very high. Viscosity for many suspensions and dilute polymer solutions becomes constant at a very high shear rate. This cannot be solved via the power-law model. (Kim,
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(a) shear-thinning fluid ( n < 1). (b) Newtonian fluid ( n = 1). (c) shear-thickening fluid ( n > 1).
3.4.2 Carreau shear thinning model
Another well-known shear thinning model is proposed by Carreau25 is provided here:
is the instantaneous viscosity, are the zero and infinite viscosities, is the time constant, is the shear rate and is the rate law index. The values for the constants are = 2.415s, n = 0.3568, = 0 0.56P and = 0.0345P
3.4.2 Cross Model
As discussed in the previous section, the power-law model does not have the capability of handling Newtonian regions of shear-thinning fluids at very low and high shear rates,In order to overcome this drawback of the power-law model, Cross (1965) proposed a model that can be described as:
where is the instantaneous viscosity, andis viscosities at very low and high shear rate , is the time constant ,m is model constants and is the shear rate .The values for the constants are, , m =1.089m ,=0 0.56P and =0.0345P
Cross model produces Newtonian viscosities at very low and shear rates compared to the Power Law model (Kim, 2002).
3.4.3 Bingham Plastic
They just forgot to mention the other effects of fluids in nature. “The influence of the fluid on a body moving through it depends not only on the body’s velocity but also on the velocity of the fluid,” this is called relative velocity ( ). The relative velocity of a body in a fluid has an effect on the magnitude of the acting forces. For example, as a long distance runner is running into a head wind, the force of the fluid is very strong. If the runner is running with the help of a tail wind, the current’s force is reduced and may even be unnoticeable.
tension of the system. Their orientation at the interface varies, depending on the components of
Working: when water ingression occurs in stern tube some kind of bio-lubricants can absorb any sea or fresh water entering the tube and form a stable emulsion thereby reduci...
Surface tension effects in wet particle assemblies cause the Liquid bridge forces. When the particle diameter is 1 mm, then these forces become dominant.
Set Parameters- FiO2 40%; Tidal Volume 70 ml; Peak Flow Auto-flow; RR 30/min; PEEP 5 cmH2O; Pressure Support 10 cmH2O; Minute Ventilation 2.1 L/min; Slope
Bernoulli’s principle is the concept that as the speed of a moving fluid (liquid or gas) increases, the pressure within that fluid decreases. This principle was originally formulated in 1738 by the Swiss mathematician and physicist Daniel Bernoulli, it states that the total energy in a steadily flowing ...
Can be calculated dynamic viscosity ƞ from the kinematic viscosity μ and the density ρ according to equation (2.1.2).
Using Mathematics to Improve Fluid Intelligence Vali Siada MARCH 2011 VOLUME 58, NUMBER 3 http://www.ams.org/notices/201103/rtx110300432p.pdf
Trefil, J. S. (1975) Introduction to the physics of fluids and solids (New York: Pergamon Press).
Mechanical Engineering 130.2 (2008): 6 - 7. Academic Search Complete. Web. The Web. The Web.
The Volume Library, vol. I, Physics: Newton's Law of Motion. Pg. 436. The Southwestern Company, Nashville, Tennessee, 1988.
This is a great discovery of Bernoulli. It seems to make sense when we apply it to blood vessels. Where the blood moves faster, the more it pushes forward, the less it pushes on the walls. A later more ingenious application for this idea is flying. The airplane was invented after Bernoulli but not due to him. The airplane and Bernoulli’s equation
The performance curves based on the ethylene glycol solution will be compared to those developed using water as the base to examine the effect, if any, the viscosity and density of the liquid has on the pump.
- the effect of Viscosity on liquid flow (turbulent/laminar) I have consulted my teachers for guidance and I have also looked very carefully into the "the Suggestions papers" which contain many possible investigations which have been done in the past. I opted to choose neither of them but many aspects I will be looking into in my investigation are similar to those in the papers.
Surface Tension: The contractive tendency of a liquid that allows it to resist an external force. This is measured in Newton.