** ** Conceptual Physics deals with the theoretical part of physics. It entails the basics that any good physician should have in order to dig deeper into more serious physics. The Bernoulli’s Principle in Conceptual Physics was formulated by Bernoulli, who obtained a relation between the pressure and velocity at different parts of a moving incompressible fluid. If the viscosity is negligibly small, there are no frictional forces to overcome. Hence the work done by the pressure difference per unit volume of a fluid flowing along a pipe steadily is equal to the gain in kinetic energy per unit volume plus the gain in potential energy per unit volume according to the Bernoulli’s principle. Engineering in Kenya has more articles.

# Its Mathematical Definition in Conceptual Physics

The work done by pressure in moving a fluid through a distance = force × distance moved = pressure × area × distance moved = pressure × volume. At the beginning of the pipe where the pressure is P1, the work done per unit volume on the fluid according to The Bernoulli’s Principle is P1. At the other end, if the pressure is P2, then the work done per unit volume according to the Bernoulli’s principle in Conceptual Physics is P2. Hence the net work done per unit volume is the difference of P2 and P1. The kinetic energy per unit volume = ½mass per unit × velocity2 = ½ρ × velocity2 where ρ is the density of the fluid. Thus if v1 and v2 are the final and initial velocities at the end and the beginning of the pipe respectively, then the kinetic energy gained per unit volume = ½ρ(v22 – v12).

Further, if h2 and h1 are the respective heights measured from a fixed level at the end and the beginning of the pipe respectively, the potential energy gained per unit volume according to the Bernoulli’s principle in Conceptual Physics is = mass per unit volume × g × (h2 – h1) = ρg(h2 – h1). Thus from the conservation of energy; P1 – P2 = ½ρ (v22 – v12) + ρg (h2 – h1). P1 + ½ρv12 + h1ρg = P2 + ½ρv22 + h2ρg. Therefore; P + ½ρv2 + hρg = constant where P is the pressure at any part and v is the velocity at that part. Hence for streamline motion of an incompressible non-viscous fluid, the Bernoulli’s principle in Conceptual Physics is proven and it states that; the sum of the pressure at any part plus the kinetic energy per unit volume plus the potential energy per unit volume is always a constant. The Bernoulli’s principle in Conceptual Physics shows that at points in a moving fluid where the potential energy change hρg is very small, or zero as in flows through a horizontal pipe, the pressure is low where the velocity is high; conversely, the pressure is high where the velocity is low according to the Bernoulli’s principle in Conceptual Physics. E.g. as a numerical illustration, suppose the area of cross-section A1 of x in the figure above is 4cm2, the area A2 of y is 1cm2 and water flows past each section in laminar (streamline) flow at the rate of 400cm3s-1, then; At x, speed v1 of water = volume per second/area = 400cm2s-1/4cm2 = 100cms-1 = 1ms-1. At y, speed v2 of water = (400cm3s-1/1cm2)400cms-1 = 4ms-1. Since the density of water is ρ = 1000 kgm-3, then the pressure difference P is; P = ½ρ (v22 – v12) = ½ × 1000 (42 – 12) = 7.5 × 103 Nm-2. Therefore; P = hρg → h = P/ρg = (7.5 × 103)/ (1000×9.8) ≈ 0.77m The pressure head is thus equivalent to 0.77m of water.