viscosity

Viscosity is internal friction in a fluid. Viscous forces oppose the motion of one portion of a fluid relative to another. Viscosity is the reason it takes effort to paddle a canoe through calm water, but it is also the reason the paddle works. Viscous effects are important in the flow of fluids in pipes, the flow of blood, the lubrication of engine parts, and many other situations

Fluids that flow readily, such as water or gasoline, have smaller viscosities than do “thick” liquids such as honey or motor oil. Viscosities of all fluids are strongly temperature dependent, increasing for gases and decreasing for liquids as the temperature increases (Fig. 12.28). Oils for engine lubrication must flow equally well in cold and warm conditions, and so are designed to have as little temperature variation of viscosity as possible.

A viscous fluid always tends to cling to a solid surface in contact with it. There is always a thin boundary layer of fluid near the surface, in which the fluid is nearly at rest with respect to the surface. That’s why dust particles can cling to a fan blade even when it is rotating rapidly, and why you can’t get all the dirt off your car by just squirting a hose at it.

Viscosity has important effects on the flow of liquids through pipes, including the flow of blood in the circulatory system. First think about a fluid with zero viscosity so that we can apply Bernoulli’s equation, Eq. (12.17). If the two ends of a long cylindrical pipe are at the same height (y₁ = y₂) and the flow speed is the same at both ends (v₁ = v₂), Bernoulli’s equation tells us that the pressure

is the same at both ends of the pipe. But this isn’t true if we account for viscosity.
To see why, consider Fig. 12.29, which shows the flow-speed profile for laminar
flow of a viscous fluid in a long cylindrical pipe. Due to viscosity, the speed is zero
at the pipe walls (to which the fluid clings) and is greatest at the center of the pipe.
The motion is like a lot of concentric tubes sliding relative to one another, with the
central tube moving fastest and the outermost tube at rest. Viscous forces between
the tubes oppose this sliding, so to keep the flow going we must apply a greater pressure
at the back of the flow than at the front. That’s why you have to keep squeezing
a tube of toothpaste or a packet of ketchup (both viscous fluids) to keep the fluid
coming out of its container. Your fingers provide a pressure at the back of the
flow that is far greater than the atmospheric pressure at the front of the flow.

The pressure difference required to sustain a given volume flow rate through
a cylindrical pipe of length L and radius R turns out to be proportional to L/R⁴
.
If we decrease R by one-half, the required pressure increases by 2⁴ = 16;
decreasing R by a factor of 0.90 (a 10% reduction) increases the required pressure
difference by a factor of (1/0.90)⁴ = 1.52 (a 52% increase). This simple
relationship explains the connection between a high-cholesterol diet (which tends
to narrow the arteries) and high blood pressure. Due to the R⁴
 dependence, even a
small narrowing of the arteries can result in substantially elevated blood pressure
and added strain on the heart muscle

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