2nd Principle : Beams and Bernoulli's Principle

Beams are long bars of rigid material used for bridging gaps. A beam is possibly the simplest example of a structure. The exaggerated sagging of the beam in the diagram highlights that, when in place, the lower half of a beam is in tension while the upper half is in compression. The tension along the lower half of the beam can only be withstood by a material that is strong and the deflection will be small only for a material with a high Young's modulus. This is why steel is favored for beams. Where concrete is used, the beam is reinforced with steel rods along its lower half. Concrete beams are even stronger if tensioned steel rods are used to prestress the concrete. A low value for the bending implies high stiffness.  

Bernoulli's Principle states that the pressure p in a fluid, in conditions of stream-line flow, satisfies the equation:

                  p + 1/2 pv2 + pgh = constant

Streamline flow is the smooth flow of a fluid without any eddies due to turbulence. It is destroyed when a fluid flows along a pipe or a canal too fast.

Notice that all the quantities in the equation are evaluated at a point; p is thrust per unit area at a point, p is mass per unit volume at a point, v is the rate of change of displacement at a point,g is the gravitational field strength at a point and h is the vertical distance of the point from a reference level.

The middle term in the expression, 1/2pv2, is called the dynamic pressure. The static pressure, p+pgh, the sum of an instrintic component p and a gravitational potential energy component pgh. The instrintic component matters more in gases, while the gravitational potential energy component is often the significant component in moving liquid masses.

In key applications, the change in level h is usually too small to be relevant and increase in speed brings about a drop in pressure. Three applications of the principle are illustrated in the diagram below:

The pressure gage is the first diagram records the higher pressure in the duct compared with the pipe; the air flows faster within the pipe than within the duct. The arrangement is the basis of carburetor design. 

The second example is the airfoil. It is so shaped that air flows faster over one surface than the other. There is a drop in pressure that gives a net force (or lift) on the airfoil from the low speed side toward the high speed side. This is the principle of the airplane wing but it explains the action, too, of sails on sailboats and their rudders.

The third example is the pitot-static tube. The tube is mounted parallel to streamlines in a moving fluid. The fluid runs past the holes in the outer tube and reduces the pressure.The inner tube has a hole facing the current and catches its full force. The reading on the pressure gage can be used to calculate the speed of the fluid.