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Creeping flow past a falling sphere in a fluid (e.g., a droplet of fog falling through the air): streamlines, drag force F d and force by gravity F g. At terminal (or settling) velocity , the excess force F e due to the difference between the weight and buoyancy of the sphere (both caused by gravity [ 7 ] ) is given by:
Here is fluid speed, is the acceleration due to gravity, is the height above some reference point, is the pressure, and is the density. In order to derive Torricelli's formula the first point with no index is taken at the liquid's surface, and the second just outside the opening.
The three terms are used to define the state of a closed system of an incompressible, constant-density fluid. When the dynamic pressure is divided by the product of fluid density and acceleration due to gravity, g, the result is called velocity head, which is used in head equations like the one used for pressure head and hydraulic head.
The flow rate can be converted to a mean flow velocity V by dividing by the wetted area of the flow (which equals the cross-sectional area of the pipe if the pipe is full of fluid). Pressure has dimensions of energy per unit volume, therefore the pressure drop between two points must be proportional to the dynamic pressure q.
Flux F through a surface, dS is the differential vector area element, n is the unit normal to the surface. Left: No flux passes in the surface, the maximum amount flows normal to the surface.
Certain valves are provided with an associated flow coefficient, commonly known as C v or K v. The flow coefficient relates pressure drop, flow rate, and specific gravity for a given valve. [10] Many empirical calculations exist for calculation of pressure drop, including: Darcy–Weisbach equation, to calculate pressure drop in a pipe
Here η is the total fluid column height (instantaneous fluid depth as a function of x, y and t), and the 2D vector (u,v) is the fluid's horizontal flow velocity, averaged across the vertical column. Further g is acceleration due to gravity and ρ is the fluid density. The first equation is derived from mass conservation, the second two from ...
In fluid mechanics, the pressure-gradient force is the force that results when there is a difference in pressure across a surface. In general, a pressure is a force per unit area across a surface. A difference in pressure across a surface then implies a difference in force, which can result in an acceleration according to Newton's second law of ...