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Control valves
Published in Raymond F. Gardner, Introduction to Plant Automation and Controls, 2020
The pressure drop across an orifice is useful for understanding control valve behavior, where a control valve is essentially an adjustable orifice. As the liquid approaches the restriction, the flow streamlines converge inward as shown in Figure 9.33. The flow continues to converge past the obstruction, so that the minimum flow area occurs downstream at the “vena contracta.” Fluid follows the continuity equation (Q=vA), so that as the flow area reduces, the velocity increases. In accordance with Bernoulli’s principle, the flow reaches maximum velocity at the vena contracta, and the pressure drops to its minimum value. Beyond the vena contracta, the streamlines expand, the flow area increases, and the velocity decelerates until the streamlines again reach the pipe wall. As the fluid decelerates, some of the pressure energy dropped at the vena contracta is recovered, where the velocity energy is converted back into pressure. However, a permanent unrecoverable pressure loss also takes place across the restriction. In accordance with the continuity equation, the velocity downstream of the orifice will be the same as upstream.
Introduction to Hydraulic Power
Published in Qin Zhang, Basics of Hydraulic Systems, 2019
Equation (1.11) is the fluid continuity equation for hydraulic jack applications. It shows that, under a certain flow rate, a smaller piston area results in a higher stroking velocity and vice versa. The fluid continuity equation is one of the fundamental equations for hydraulic system analysis. To apply the fluid continuity equation in fluid distribution analysis without loss of generality, the control volume of fluid in a “T” connector, commonly seen in practical fluid power systems, is shown in Figure 1.7. The fluid continuity equation for this “T” connector can be written as follows: q1=v1A1=v2A2+v3A3=q2+q3
Airflow Modeling and Particle Control by Vertical Laminar Flow
Published in R. P. Donovan, Particle Control for Semiconductor Manufacturing, 2018
The continuity equation follows from the conservation of mass, which states that the change of fluid mass in any fixed volume element equals the rate of mass flow in or out of that element. When the fluid density is constant in time and position (an incompressible fluid), the continuity equation takes the form shown in Equation (18-3).
Simulating the structure and air permeability of needle-punched nonwoven layer
Published in The Journal of The Textile Institute, 2018
H. Dabiryan, M. Karimi, S. Mohammad Hosseini Varkiani, S. Nazeran
The Navier–Stokes equations describe the motion of viscous fluid substances. In fluid dynamics, the continuity equation is an expression of conservation of mass. In (vector) differential form, it is written as (White, 2009):