Forces associated with the system model, body (point mass or extended body) , were the gravity force acting on the mass at its location and external forces. The gravity force was mass times gravity and the surface forces were F...
Newton's conclusions regarding motion without friction extend in a natural way to the new model and perspective, "ideal fluid." Ideal fluids, (gases or liquids,) have extent, are frictionless, deformable and uniformly distributed.
Newton studied "bodies in motion without friction." His construct, force, applied readily to the system models "point mass" or "extended body." His conclusions extend in a natural way to "fluid motion without friction." The new model perspective required is the "ideal fluid," which is "deformable and distributed." Also, to deal with fluid motion requires modification of the construct, force. Systems of ideal fluid either flow (or do not flow) in accord with the forces, gravity and boundary forces, that act on them. The forces are related to the fluid properties density and pressure.
DENSITY, VOLUME AND GRAVITY FORCE: The masses of ideal fluids are distributed over the spaces they occupy in accord with the action of gravity. The density of atmospheric air varies with altitude but in most other circumstances density, the fluid mass divided by its space, [m/L³], is uniform. There are many manners of measuring fluid density.
Gravity force acts on all differential elements of a fluid. In drawing the free body of a fluid system, the summed effect of gravity forces (F = ∫ρgodV) is represented as a single force located at the center of mass directed toward Earth. Unconstrained gravity forces will cause a fluid to flow "downhill" as we say. In the case of gas-liquid contact, the liquid upper surface will attain a locally horizontal aspect.
Density with the dimensions [m/L³] is defined as the mass within a selected volume, divided by that volume as it becomes "vanishingly small."
That last ratio of mass to volume is the fluid density which has many manners of measurement. The body force that acts on a fluid, acts on all of its differential elements of volume, ΔV, and is directed downward toward Earth. The magnitude of the differential body force is: ρgΔV. The increments of gravity force of a fluid have the same form, permitting them to be summed to over all volume elements.
Fbody, fluid system = ΣρgΔV. In drawing a free body diagram, one draws the gravity force as a single force located at the center of mass of the fluid.
PRESSURE, AREA AND PRESSURE-FORCE The fluid system boundary is that extreme outer collection of particles that impact the boundary and exchange momentum with it. The collective momentum exchange of the particle interactions is called pressure with dimensions [F/L2]. Pressure is a property of a fluid system in its interior and at all points on its surface. Pressure acting over a differential area (ΔA) amounts to what is called pressure-force, with dimension mL/t2] or [F] . Pressure forces act perpendicular to the system surface and are directed toward the fluid system.
| DENSITIES (@ 1 atm, 25°C) | |
| Substance | Density ~ kg/m3(lbm/ft3) |
|---|---|
| air | 1.2 kg/m3 (0.075) |
| water (liquid) water (solid) |
1000 kg/m3 (62.4) 920 kg/m3(490) |
| mercury | 13560 kg/m3 () |
| sea water | 1025 kg/m3 (64) |
| Earth soils | 1920 kg/m3 (120) |
| concrete | 2400 kg/m3 (150) |
| iron or steel | 7850 kg/m3 (490) |
| Use Water for Unit Conversions 1000 kg/m3 ≡ 62.4 lbm/ft3 |
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The vast numbers of particles of an ideal fluid experience continuous collision and momentum exchange over all incremental areas of their boundaries. The surrounding participate in the momentum exchange by exerting incremental forces perpendicular to the increments of boundary area (ΔA). During analysis of fluid systems, it is helpful to represent pressure forces that exist at the system boundary. To that purpose, small arrows are drawn directed toward and perpendicular to the system surface where they are located. The arrows do not represent pressure. Rather they represent an increment of force having the magnitude, pressure times incremental area, perpendicular to the surface. Pressure and hence, pressure force, acts continuously over all of the area of fluid boundaries.