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The viscous friction causes the flow properties to change along the duct. The frictional effect is modeled as a shear stress at the wall acting on the fluid with uniform properties over any cross section of the duct. For a flow with an upstream Mach number greater than 1.0 in a sufficiently long duct, deceleration occurs and the flow can become ...
The choked velocity is a function of the upstream pressure but not the downstream. Although the velocity is constant, the mass flow rate is dependent on the density of the upstream gas, which is a function of the upstream pressure. Flow velocity reaches the speed of sound in the orifice, and it may be termed a sonic orifice.
The case of a converging-diverging nozzle allows a supersonic flow to occur, providing the receiver pressure is sufficiently low. This is shown in figure 3 assuming a constant reservoir pressure with a decreasing receiver pressure. If the receiver pressure is equal to the reservoir pressure, no flow occurs, represented by curve A.
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.
A supersonic diffuser is a duct that decreases in area in the direction of flow which causes the fluid temperature, pressure, and density to increase, and velocity to decrease. These changes occur because the fluid is compressible. Shock waves may also play an important role in a supersonic diffuser.
For this model, the duct area remains constant and no mass is added within the duct. Therefore, unlike Fanno flow , the stagnation temperature is a variable. The heat addition causes a decrease in stagnation pressure , which is known as the Rayleigh effect and is critical in the design of combustion systems.
In fluid dynamics, dynamic pressure (denoted by q or Q and sometimes called velocity pressure) is the quantity defined by: [1] = where (in SI units): q is the dynamic pressure in pascals (i.e., N/m 2, ρ (Greek letter rho) is the fluid mass density (e.g. in kg/m 3), and; u is the flow speed in m/s.
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 ...