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In mechanics, a diaphragm is a sheet of a semi-flexible material anchored at its periphery and most often round in shape. It serves either as a barrier between two chambers, moving slightly up into one chamber or down into the other depending on differences in pressure , or as a device that vibrates when certain frequencies are applied to it.
The basic working principle of an air-operated double diaphragm pump. Cross-section sketch of diaphragm fuel pump Air-operated double diaphragm pump. A diaphragm pump (also known as a Membrane pump) is a positive displacement pump that uses a combination of the reciprocating action of a rubber, thermoplastic or teflon diaphragm and suitable valves on either side of the diaphragm (check valve ...
This is a crucial parameter for pump selection and is a popularly used parameter for ascertaining industrial requirements. By eliminating the inlet head, we remove the effect of the supplied pressure to the pump and are left with only the pump’s energy (head) contribution to the fluid flow. Schematic representation of pressure heads in a pump.
In the following we solve the second-order differential equation called the hypergeometric differential equation using Frobenius method, named after Ferdinand Georg Frobenius. This is a method that uses the series solution for a differential equation, where we assume the solution takes the form of a series. This is usually the method we use for ...
where is the Gauss map, and the differential of regarded as a vector-valued differential form, and the brackets denote the metric tensor of Euclidean space. More generally, on a Riemannian manifold, the second fundamental form is an equivalent way to describe the shape operator (denoted by S ) of a hypersurface,
Then for an ideal gas the compressible Euler equations can be simply expressed in the mechanical or primitive variables specific volume, flow velocity and pressure, by taking the set of the equations for a thermodynamic system and modifying the energy equation into a pressure equation through this mechanical equation of state. At last, in ...
The above equation can be used to plot the Rayleigh line on a Mach number versus ΔS graph, but the dimensionless enthalpy, H, versus ΔS diagram, is more often used. The dimensionless enthalpy equation is shown below with an equation relating the static temperature with its value at the choke location for a calorically perfect gas where the ...
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a ...