Suction pressure equation

B. The Process of Elongation Within a Cell 1. The Suction Pressure Equation of the Cell... 

We seem to have digressed somewhat from our discussion of elongation. However the connection becomes clear immediately when we mention the fact that in elongation the vacuoles or the single central space for cell sap are expanded quite considerably by water uptake. Water uptake implies an increase in the suction pressure of the cell. According to the suction pressure equation Sc=Sj-W, this increase can be attained by either a rise in the osmotic pressure of the cell sap SfOX a decrease in the wall pressure W. 

The terms pressure ratio and volume ratio are used interchangeably in the literature on these machines. To prevent confusion, volume ratio t , is defined as the volume of the trapped gas at the start of the compression cycle divided by the volume of the gas just prior to the opening of the discharge port. Pressure ratio is defined, in Equation 2.64, as the discharge pressure divided by the suction pressure. Their relationship is given in the following equation. 

Continue for number of terms on right side of equation equal to number of stages. This is usually best solved by trial and error and can be simplified if most of the AP values are assumed equal. It assumes all the intercooler pressure drop is deducted from the suction pressure of the succeeding stage, i.e., first stage intercooler pressure drop is deducted from second stage suction pressure. 

This equation is to be used only for this step in the evaluation of volumetric efficiency and should not be used for any other factor in the performance evaluation. Due to valve and other losses being a significant portion in low suction pressure (less than 10 psig) cylinder performance, this can result in reduced performance if not corrected as noted. 

The pressure p used in Equation 3-32 is the differential developed pressure (across the pump inlet and outlet). Since the inlet suction pressure is usually small compared to the discharge pressure, the discharge pressure is used. Thus, this is the application resistance pressure in most cases. Figure. 3-54 shows a typical reciprocating pump performance. 

The suction pressure Ps is determined by applying the Bernoulli equation to the suction line upstream of the pump. For example, if the pressure at the entrance to the upstream suction line is P1 the maximum distance above this point that the pump can be located without cavitating (i.e., the maximum suction lift) is determined by Bernoulli s equation from Px to Ps ... 

In the two examples we have just discussed, you should have noticed, that Pv the compressor suction pressure, was not being held constant. In fact, when the molecular weight of the gas increased, Pv the suction pressure, went down. Let me now rewrite Robert Mayer s equation, which I presented at the start of this chapter ... 

A variant is the micro-pipette method, which is also similar to the maximum bubble pressure technique. A drop of the liquid to be studied is drawn by suction into the tip of a micropipette. The inner diameter of the pipette must be smaller than the radius of the drop the minimum suction pressure needed to force the droplet into the capillary can be related to the surface tension of the liquid, using the Young-Laplace equation [1.1.212). This technique can also be used to obtain interfacial tensions, say of individual emulsion droplets. Experimental problems include accounting for the extent of wetting of the inner lumen of the capillary, rate problems because of the time-dependence of surfactant (if any) adsorption on the capillary and, for narrow capillaries accounting for the work needed to bend the interface. Indeed, this method has also been used to measure bending moduli (sec. 1.15). 

In this model also the decrease of the pore radius due to the formation of an adsorbed layer is incorporated. Flow 1 in Fig. 9.9 is the case of combined Knudsen molecular diffusion in the gas phase and multilayer (surface) flow in the adsorbed phase. In case 2, capillary condensation takes place at the upstream end of the pore (high pressure Pi) but not at the downstream end (P2), and in case 3 the entire capillary is filled with condensate. The crucial point in cases 3 and 4 is that the liquid meniscus with a curved surface not only reduces the vapour pressure (Kelvin equation) but also causes a hydrostatic pressure difference across the meniscus and so causes a capillary suction pressure Pc equal to... 

Using a micropipette and a small suction pressure to aspirate a hemispherical projection from a cell body into the pipette, Evans and Yeung measured a value for the cortical tension of 0.035 mN/m. Needham and Eiochmuth [1992] measured the cortical tension of individual cells that were driven down a tapered pipette in a series of equilibrium positions. In many cases the cortical tension increased as the cell moved further into the pipette, which means that the ceU has an apparent area expansion modulus (Equation 60.7). They obtained an average value of 0.04 mN/m for the expansion modulus and an extrapolated value for the cortical tension (at zero area dilation) in the resting state of 0.024 mN/m. The importance of the actin cytoskeleton in maintaining cortical tension was demonstrated by Tsai et al. [ 1994]. Treatment of the cells with a drug that disrupts actin filament structure (CTB = cytochalasin B) resulted in a decrease in cortical tension from 0.027 to 0.022 mN/m at a CTB concentration of 3 /rM and to 0.014 mN/m at 30 /rM. 

Power requirements can be estimated based on the flowrate (FDA equiva-ient) and the suction pressure. This method uses the equation below and is approximate only although it correlates well with test data especially for liquidring pumps. Suction pressures should be limited to the range of 10 to 500 torr. 

Equations (6.9) and (6.12) indicate that the consolidation rate increases with the capillary suction pressure p of the mold. If there were no other effects, an increase in p would always lead to a shorter time for a given thickness of the cast. The capillary suction pressure varies inversely as the pore radius of the mold, and it may be thought that a decrease in the pore radius would lead to an increase in the casting rate. However, the permeability of the mold K also decreases with a decrease in the pore radius of the mold, so there should be an optimum pore size to give the maximum rate of casting (39). 

The ordinate for both plots in Fig. 9.14 is discharge-suction pressure ratio pd/ps, starting from 1.0, or pd/ps — 10 the abscissa F is the volumetric flow at suction conditions. The locus of the surge line varies with suction temperature and can be represented by the equation... 

Cavitation Loosely regarded as related to water hammer and hydrauhc transients because it may cause similar vibration and equipment damage, cavitation is the phenomenon of collapse of vapor bubbles in flowing liquid. These bubbles may be formed anywhere the local liquid pressure drops below the vapor pressure, or they may be injected into the hquid, as when steam is sparged into water. Local low-pressure zones may be produced by local velocity increases (in accordance with the Bernouhi equation see the preceding Conservation Equations subsection) as in eddies or vortices, or near bound-aiy contours by rapid vibration of a boundaiy by separation of liquid during water hammer or by an overaU reduction in static pressure, as due to pressure drop in the suction line of a pump. 

NPSH calculations might have to be modified if there are significant amounts of dissolved gas in the pump suction liquid. See Suction System NPSH Available" in this handbook for calculations when dissolved gas does not need to be considered. In that case the suction liquid s vapor pressure is a term in the equation. With dissolved gases, the gas saturation pressure is often much higher than the liquid s vapor pressure. 

The pressure at any point in the suction line must never be reduced to the vapor pressure of the liquid (see Equation 3-6). Both the suction head and the vapor pressure must be expressed in feet of the liquid, and must both be expressed as gauge pressure or absolute pressure. Centrifugal pumps cannot pump any quantity of vapor, except possibly some vapor entrained or absorbed in the liquid, but do not count cm it. The liquid or its gases must not vaporize in the eye/entrance of the impeller. (This is the lowest pressure location in the impeller.)... 

Most state laws and safe practice require a safety relief valve ahead of the first stop valve in every positive displacement compressed air system. It is set to release at 1.25 times the normal discharge pressure of the compressor or at the maximum working pressure of the system, whichever is lower. The relief valve piping system sometimes includes a manual vent valve and/or a bypass valve to the suction to facilitate startup and shutdown operations. Quick line sizing equations are (1) line connection, (i/1.75 (2) bypass, ii/4.5 (3) vent, dl63 and (4) relief valve port, cU9. 

Since, in general, lower permeability media exhibit higher capillary-pressure suction, we argue that it is more difficult to stabilize foam when the permeability is low. Indeed the concept of a critical capillary pressure for foam longevity can be translated into a critical permeability through use of the universal Leverett capillary-pressure J-function (.13) and, by way of example, the constant-charge model in Equation 2 for II ... 

In equation 4.2, hfs is the head loss due to friction, zs is the static head and Ps is the gas pressure above the liquid in the tank on the suction side of the pump. If the liquid level on the suction side is below the centre-line of the pump, zs is negative. 

It is clear from equation 4.2 that the suction head hs can fall to a very low value, for example when the suction frictional head loss is high and the static head zs is low. If the absolute pressure in the liquid at the suction flange falls to, or below, the absolute vapour pressure Pv of the liquid, bubbles of vapour will be formed at the pump inlet. Worse still, even if the pressure at the suction flange is slightly higher than the vapour pressure, cavitation—the formation and subsequent collapse of vapour bubbles— will occur within the body of the pump because the pressure in the pump falls further as the liquid is accelerated. 

Equation 4.10 shows that when a centrifugal pump runs on air, the pressure developed is very small. In fact, a conventional centrifugal pump can never prime itself when operating on a suction lift. 

The term capillary action describes the upward movement of a fluid as a result of surface tension through pore spaces. The fluid can rise until the lifting forces are balanced by gravitational pull (see Figure 3.28). The rise of fluid in a small tube above the water table surface, as previously discussed in Chapter 3, can be described using Equation 3.13. Lifting of fluids above the water table is a true negative pressure compared with atmospheric pressure (also described as soil suction). In soil situa-... 

Equation (5.52) is Bernoulli s theorem [16], an energy equation that is well known to be equal to the sum of the elevation head, the pressure head, and the velocity head. Here the elevation head has been left out because the fan suction air pressure and the exiting air pressure from the air cooler are both equal. 

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