Viscous Resistance

Though the theory of viscosity has a number of applications, yet the viscous resistance on bearings is important. The following points may be noted for viscous resistance:

(a) Torque required to overcome viscous resistance of footstep bearing is:



N = Speed of the shaft,
R = Radius of the shaft, and
t = Thickness of the oil film.

(b) Torque required to overcome viscous resistance of a collar bearing is


where

R1 and R2 = External and internal radius of collar.

(c) The coefficient of viscosity may be found out, experimentally, by the following methods:

(i) Capillary tube method
(ii) Orifice type viscometer;
(iii) Rotating cylinder method; and
(iv) Falling sphere method.

(d) The coefficient of viscosity (in poises), according to the method of orifice type viscometer, is

Compressible Flow of Fluids

We have already discussed that for an in-compressible fluid flow, the total quantity of flow at different sections of a pipe is same, i.e.


But in a compressible fluid flow, the mass of fluid flowing through any section of the pipe is same, i.e.,

Velocity of Sound Wave

The velocity of sound in a fluid is given by



where

K = Bulk modulus, and
p = Density of the fluid.

Mach Number and its Importance

What is Mach Number and importance of Mach Number? The ratio of velocity of fluid, in an undisturbed stream, to the velocity of sound wave, is known as Mach number. It gives us an important information about the type of flow. In general, the flow of a fluid is divided into the following four types depending upon the Mach number.

(a) When the Mach number is less than unity, the flow is called a sub-sonic flow.
(b) When the Mach number is equal to unity, the flow is called a sonic flow.
(c) When the Mach number is between 1 and 6, the flow is called a supersonic flow.
(d) When the Mach number is more than 6, the flow is called hypersonic flow.

Stagnation Point

What is a stagnation point in fluid dynamics? A point in the flow, where the velocity of fluid is zero, is called a stagnation point. Stagnation points exist at the surface of objects in the flow field, where the fluid is brought to rest by the object. The Bernoulli equation shows that the static pressure is highest when the velocity is zero and hence static pressure is at its maximum value at stagnation points. This static pressure is called the stagnation pressure.

Flow Around Immersed Bodies

Flow Around Immersed Bodies - We see that when a solid body is held in the path of a moving fluid and is completely immersed in it, the body will be subjected to some pressure or force. Conversely, if a body is moved with a uniform velocity through a fluid at rest, it offers some resistance to the moving body or the body has to exert some force to maintain its steady movement.

According to Newton's law of resistance, the force exerted by a moving fluid on an immersed body is directly proportional to the rate of change of momentum due to the presence of the body.

The following points may be noted for the flow around immersed bodies:

(a) Whenever a plate is held immersed at some angle with the direction of the flow of the liquid, it is subjected to some pressure. The component of this pressure, in the direction of the flow of the liquid, is known as drag and the component of this pressure at right angles to the direction of the flow of the liquid is known as lift.

(b) According to Prandtl - Blasius relation, the thickness of boundary layer in laminar flow is



and thickness of boundary layer in a turbulent flow,



where

x = Distance between the leading edge of the body and the section where thickness of boundary layer is required, and
Rnx = Reynold’s number at a distance x from the leading edge.

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