# Fluid flow

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## Fluid flow

Motion of a fluid subjected to unbalanced forces or stresses. The motion continues as long as unbalanced forces are applied. For example, in the pouring of water from a pitcher the water velocity is very high over the lip, moderately high approaching the lip, and very low near the bottom of the pitcher. The unbalanced force is gravity, that is, the weight of the tilted water particles near the surface. The flow continues as long as water is available and the pitcher remains tilted. *See* Fluids

A fluid may be a liquid, vapor, or gas. The term vapor denotes a gaseous substance interacting with its own liquid phase, for example, steam above water. If this phase interaction is not important, the vapor is simply termed a gas.

Gases have weak intermolecular forces and expand to fill any container. Left free, gases expand and form the atmosphere of the Earth. Gases are highly compressible; doubling the pressure at constant temperature doubles the density.

Liquids, in contrast, have strong intermolecular forces and tend to retain constant volume. Placed in a container, a liquid occupies only its own volume and forms a free surface which is at the same pressure as any gas touching it. Liquids are nearly incompressible; doubling the pressure of water at room temperature, for example, increases its density by only 0.005%.

Liquids and vapors can flow together as a mixture, such as steam condensing in a pipe flow with cold walls. This constitutes a special branch of fluid mechanics, covering two-phase-flow.

The physical properties of a fluid are essential to formulating theories and developing designs for fluid flow. Especially important are pressure, density, and temperature.

Since shear stresses cause motion in a fluid and result in differences in normal stresses at a point, it follows that a fluid at rest must have zero shear and uniform pressure at a point. This is the hydrostatic condition. The fluid pressure increases deeper in the fluid to balance the increased weight of fluid above. For liquids, and for gases over short vertical distances, the fluid density can be assumed to be constant. *See* Hydrostatics

When a fluid is subjected to shear stress, it flows and resists the shear through molecular momentum transfer. The macroscopic effect of this molecular action, for most common fluids, is the physical property called viscosity. Shear stress results in a gradient in fluid velocity; the converse is also true.

The common fluids for which the linear relationship of flow velocity and sheer stress holds are called newtonian viscous fluids. More complex fluids, such as paints, pastes, greases, and slurries, exhibit nonlinear or non-newtonian behavior and require more complex theories to account for their behavior. *See* Newtonian fluid, Non-newtonian fluid, Viscosity

A common characteristic of all fluids, whether newtonian or not, is that they do not slip at a solid boundary. No matter how fast they flow away from the boundary, fluid particles at a solid surface become entrapped by the surface structure. The macroscopic effect is that the fluid velocity equals the solid velocity at a boundary. This is called the no-slip condition where the solid is fixed, so that the fluid velocity drops to zero there. No-slip sets up a slow-moving shear layer or boundary layer when fluid flows near a solid surface. The theory of boundary-layer flow is well developed and explains many effects involving viscous flow past immersed bodies or within passages. *See* Boundary-layer flow

All fluids are at least slightly compressible, that is, their density increases as pressure is applied. In many flows, however, compressibility effects may be neglected. A very important parameter in determining compressibility effects is the Mach number Ma, or ratio of flow velocity *V* to fluid speed of sound. For subsonic flow, Ma < 1, whereas for supersonic flow, Ma > 1. The flow is essentially incompressible if Ma < 0.3; hence for air the flow velocity is less than about 100 m/s (330 ft/s). Almost all liquid flows and many gas flows are thus treated as incompressible. Even a supersonic airplane lands and takes off in the incompressible regime. *See* Compressible flow, Mach number

For various types of fluid flow *See* Fluid mechanics, Hydrodynamics, Isentropic flow, Laminar flow, Rarefied gas flow, Turbulent flow, Wake flow