Question
Tue January 18, 2011 By: Archit Srivastava
 

in resnick halliday book i read that when a fluid is in contact with a surface,the pressure is exerted by the fluid molecules by the collisions between molecules and contact surface.It is said that as a result of collision,the component of molecule's moomentum perpendicular to the surface is reversed.what does it mean.can you elaborate.

Expert Reply
Wed January 19, 2011
Dear student,
 
It is something like this ...why does the angle of (reflection off the ground) of a tennis ball equal its angle of incidence?

A photon ( fluid molecule, say) has momentum so when it strikes the mirror ( or  wall) the component of momentum perpendicular to the mirror surface will be reversed but not the parallel component. Hence the angle of incidence = angle of reflection (just like a tennis ball).
 
Let us discuss in detail.

Molecular Definition of Pressure

From the kinetic theory of gases, a gas is composed of a large number of molecules that are very small relative to the distance between molecules. The molecules of a gas are in constant, random motion and frequently collide with each other and with the walls of any container. The molecules possess the physical properties of mass, momentum, and energy. The momentum of a single molecule is the product of its mass and velocity, while the kinetic energy is one half the mass times the square of the velocity. As the gas molecules collide with the walls of a container, as shown on the left of the figure, the molecules impart momentum to the walls, producing a force perpendicular to the wall. The sum of the forces of all the molecules striking the wall divided by the area of the wall is defined to be the pressure. The pressure of a gas is then a measure of the average linear momentum of the moving molecules of a gas. The pressure acts perpendicular (normal) to the wall; the tangential (shear) component of the force is related to the viscosity of the gas.

Scalar Quantity

Let us look at a static gas; one that does not appear to move or flow. While the gas as a whole does not appear to move, the individual molecules of the gas, which we cannot see, are in constant random motion. Because we are dealing with a nearly infinite number of molecules and because the motion of the individual molecules is random in every direction, we do not detect any motion. If we enclose the gas within a container, we detect a pressure in the gas from the molecules colliding with the walls of our container. We can put the walls of our container anywhere inside the gas, and the force per area (the pressure) is the same. We can shrink the size of our "container" down to an infinitely small point, and the pressure has a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has a magnitude but no direction associated with it. Pressure acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular to the surface.

Hope this helps.

Team

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