Nozzle fluid flow, pressure drop

Fig. 9 Schematic of SEDS process showing coaxial nozzles. Solvent containing drug is introduced into a stream of SC fluid, using a two or three fluid coaxial nozzle design with mixing chamber. The high velocity and turbulence of the SC fluid stream causes the solvent solution to break up into small droplets. The SC fluid extracts the solvent, acting as the antisolvent for the compound, leading to a supersaturated state and precipitation of drug particles. Control over the size of the particles is achieved by controlling the flow rates of the input streams to the nozzle, and the pressure drop across the nozzle. Typical mean particle sizes are 1-20 pm in a narrow particle size distribution. (From Palakodaty, S., Walker, S., Townend, G., York, P., Humphreys, G. Eur. Pharm. Contractor 2000, (Aug), 60-63.)...

Now consider the pressure drops that occur during rapid expansion. Applying the Bernoulli equation for an inviscid, incompressible fluid, we can readily show that the pressure drop from pre-expansion conditions to the initiation of rapid expansion (i.e., from Pq to Fini) is smaller by a factor of 10 than the pressure drop from pre-expansion conditions to the nozzle outlet (i.e., from Po to P2). Now for a typical RESS application, the pre-expansion pressure Po is about 200 bar. Because of the choked-flow conditions that exist at the nozzle exit, the pressure drop is about 100 bar. Accordingly, the pressure at Zini (i.e., Fini) is only about 0.01 bar less than Fq for incompressible flow, and the pressure drop... 

In liquid ejectors or aspirators, the hquid is the motive fluid, so the gas pressure drop is low. Flow of slurries in the nozzle may be erosive. Otherwise, the design is as simple as that of the Venturi. 

Flow through chokes and nozzles is a special case of fluid dynamics. For incompressible fluids the problem can be handled by mass conservation and Bernoulli s equation. Bernoulli s equation is solved for the pressure drop across the choke, assuming that the velocity of approach and the vertical displacement are negligible. The velocity term is replaced by the volumetric flow rate times the area at the choke throat to yield... 

The simplest and most common device for measuring flow rate in a pipe is the orifice meter, illustrated in Fig. 10-7. This is an obstruction meter that consists of a plate with a hole in it that is inserted into the pipe, and the pressure drop across the plate is measured. The major difference between this device and the venturi and nozzle meters is the fact that the fluid stream leaving the orifice hole contracts to an area considerably smaller than that of the orifice hole itself. This is called the vena contracta, and it occurs because the fluid has considerable inward radial momentum as it converges into the orifice hole, which causes it to continue to flow inward for a distance downstream of the orifice before it starts to expand to fill the pipe. If the pipe diameter is D, the orifice diameter is d, and the diameter of the vena contracta is d2, the contraction ratio for the vena contracta is defined as Cc = A2/A0 = (d2/d)2. For highly turbulent flow, Cc 0.6. 

The flow of fluids is most commonly measured using head flowmeters. The operation of these flowmeters is based on the Bernoulli equation. A constriction in the flow path is used to increase the flow velocity. This is accompanied by a decrease in pressure head and since the resultant pressure drop is a function of the flow rate of fluid, the latter can be evaluated. The flowmeters for closed conduits can be used for both gases and liquids. The flowmeters for open conduits can only be used for liquids. Head flowmeters include orifice and venturi meters, flow nozzles, Pitot tubes and weirs. They consist of a primary element which causes the pressure or head loss and a secondary element which measures it. The primary element does not contain any moving parts. The most common secondary elements for closed conduit flowmeters are U-tube manometers and differential pressure transducers. 

The pressure drop of a fluid flowing through a nozzle is equal to... 

The other method is the velocity head method. The term V2/2g has dimensions of length and is commonly called a velocity head. Application of the Bernoulli equation to the problem of frictionless discharge at velocity V through a nozzle at the bottom of a column of liquid of height H shows that H = V2/2g. Thus II is the liquid head corresponding to the velocity V. Use of the velocity head to scale pressure drops has wide application in fluid mechanics. Examination of the Navier-Stokes equations suggests that when the inertial terms dominate the viscous terms, pressure gradients are expected to be proportional to pV2 where V is a characteristic velocity of the flow. 

Both gas flow rates and liquid flow rates can be measured by a wide variety of devices such as bellow meters, Venturi nozzles, nutating disk meters, orifice meters, rotameters, weirs (for liquids), Pitot tubes, and magnetic meters among others. Some devices measure volumetric flow directly as with meters in which the space between rotating paddles incorporates small volumetric displacements of fluid. Other device measure the flows indirectly by measuring the pressure drop caused by an orifice between two different sites in the pipe, or the change in voltage of a heated wire. 

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