Formulas pressure

Yield Strength Collapse Pressure Formula. The yield strength collapse pressure is not a true collapse pressure but rather the external pressure p that generates minimum yield stress on the inside wall of a tube as calculated by... 

Plastic Collapse Pressure Formula. The minimum collapse pressure for the plastic range of collapse is calculated by... 

The factors F and G and applicable D/t range for the transition collapse pressure formula are shown in Tables 4-152 and 4-151, respectively. 

It is essential that h and D be expressed in similar units. That is, if D is expressed in pounds per cubic foot, the value of h must be expressed in feet. If the desired pressure is to be expressed in pounds per square inch, the pressure formula becomes ... 

The trend in the f-pressure is almost parabolic with band filling and this is typical for a transition metal (with d replaced by f). The physical basis was given by the Friedel who assumed that a rectangular density of states was being filled monotonically and thus was able to reproduce the parabolic trend in transition metal cohesive energies analytically. Pettifor has shown that the pressure formula can similarly be integrated analytically. 

Self-consistent energy band calculations have now been made through the LMTO method for all of the NaCl-type actinide pnictides and chalcogenides . The equation of state is derived quite naturally from these calculations through the pressure formula extended to the case of compounds . The theoretical lattice parameter is then given by the condition of zero pressure. 

This expression is produced also by integration of the well-known vapour pressure formula of Clapeyron ... 

By extrapolating with the vapour pressure formula ( 10.VIIIL) ... 

Over small ranges of temperature (not more than 10 ) the vapour pressures may be interpolated logarithmically as follows at 10°, p=9 205 mm. and log p=0 96402, at 11°,/7=9 840 mm. and log / =0 99299 difference for 1°= 0-02897, for 0-1° 0-0029, for 0-6° 0-01740 logp at 10-6°=0-98142, p=9-581 mm. For large temperature differences a vapour pressure formula ( 18-21,VIIIJ) should be used. Vapour pressures of heavy water (deuterium oxide D2O) are smaller than those of ordinary water. 1 The vapour pressure of mercury is particularly important and has often been determined some values are given below ( °C.) ... 

Pales and Shapiro (by analogy with their vapour pressure formula, 22.VIIC) ... 

We shall show in the next paragraph that the vapour pressure constants play an important part in the calculation of chemical equilibria in gases. The first problem which Nernst had to solve after the discovery of his theorem was therefore the calculation of at least the approximate value of C for as many simple substances as possible. For this purpose he made use of the theorem of corresponding states, and assumed further that the specific heat of solid and liquid bodies diminishes to a small but finite value (viz. nx 1 5, where n is the number of atoms in the molecule) as the temperature is lowered. On the evidence of the measurements published up to that time he also assumed that the molecular specific heat of gases and vapours is a linear function of the temperature which approaches the value 3-5-l-7ixl-5 at very low temperatures. In this way he arrived at the vapour pressure formula... 

You have experienced the consequences of this formula in many real-life situations. Think of the shape of a nail. The head of a nail is relatively broad, meaning that the area that you strike with a hammer is relatively large. The formula for pressure shows us that, by increasing the area of the surface of the head of the nail, we decrease the pressure per unit of area. The tip of a nail, which is designed to plunge into a wood surface, is relatively small. The pressure formula shows us that when the area is small, we exert a relatively large pressure per unit of area. 

Another example of where this formula comes into play involves a person standing on a frozen lake when the ice starts to crack. You may have heard that it is advisable to lie down on the surface of the ice, if you find yourself in this situation. The logic behind this can be seen in the pressure formula. By lying down on the surface of the ice, you will increase the area of your body that is in contact with the ice. Because the pressure that you exert on the surface of the ice is inversely proportional to the area of contact, you will be less likely to break through. 

For instance, for a 304 stainless steel welded seam pipe with an outside diameter of 3V2", to find the maximum internal pressure allowed for this pipe, use the pressure formula. Find what is called the stress value for a particular material (in this case 304 stainless steel) which is based on that material and the way it was fabricated - whether it is seamless, continuous welded, electric resistance welded, or electric fusion-arc welded. Most of the materials that you will run into will be ERW (electric resistance welded ) and thus have a seam, or will be seamless with no weld. The same material of a given diameter and thickness will be able to withstand higher internal pressure if it is seamless. 

For liquid discharges, the design of the pipework may be complex. If the liquid is subcooled, the discharge pipework is sized by standard liquid pressure formulae. If the liquid in the equipment is at or near its saturation pressure, the relief device and discharge pipework should be sized for two-phase flow. As the liquid flows through the relief valve. 

Further we have already seen (p 74) that the integration of the Clapeyron vapour pressure formula leads to values of C, the concentration of saturated vapour, which can be expressed for a single substance by the relation—... 

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