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In this expression for Reynolds number, the characteristic length D is taken to be the hydraulic diameter of the pipe, which, for a cylindrical pipe flowing full, equals the inside diameter. In Figures 1 and 2 of friction factor versus Reynolds number, the regime Re < 2000 demonstrates laminar flow; the friction factor is well represented by ...
The shear rate at the inner wall of a Newtonian fluid flowing within a pipe [2] is ˙ =, where: ˙ is the shear rate, measured in reciprocal seconds; v is the linear fluid velocity; d is the inside diameter of the pipe.
Both pipe and tube imply a level of rigidity and permanence, whereas a hose is usually portable and flexible. A tube and pipe may be specified by standard pipe size designations, e.g., nominal pipe size, or by nominal outside or inside diameter and/or wall thickness. The actual dimensions of pipe are usually not the nominal dimensions: A 1-inch ...
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.
R is the pipe radius, A is the cross-sectional area of pipe. The equation does not hold close to the pipe entrance. [8]: 3 The equation fails in the limit of low viscosity, wide and/or short pipe. Low viscosity or a wide pipe may result in turbulent flow, making it necessary to use more complex models, such as the Darcy–Weisbach equation.
In fluid dynamics, the Knudsen equation is used to describe how gas flows through a tube in free molecular flow.When the mean free path of the molecules in the gas is larger than or equal to the diameter of the tube, the molecules will interact more often with the walls of the tube than with each other.
For cylindrical pressure vessels, the normal loads on a wall element are longitudinal stress, circumferential (hoop) stress and radial stress. The radial stress for a thick-walled cylinder is equal and opposite to the gauge pressure on the inside surface, and zero on the outside surface. The circumferential stress and longitudinal stresses are ...
For the thin-walled assumption to be valid, the vessel must have a wall thickness of no more than about one-tenth (often cited as Diameter / t > 20) of its radius. [4] This allows for treating the wall as a surface, and subsequently using the Young–Laplace equation for estimating the hoop stress created by an internal pressure on a thin-walled cylindrical pressure vessel: