Pressure maximum

The blast wave produced by an explosion is caused by two mechanisms, the heating of the reaction products and the change in mole number. If an explosion progresses so fast that the volume at first remains unchanged and we deal with ideal gases the maximum pressure, ps, is obtained as follows [42] 

Substance Molar mass in g Chemical formula Loading density in g/cm Oxygen balance in % Detonation velocity Vj, in m/s  

According to [43] the maximum pressure may also be obtained from 

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Beside all technical reasons the big advantage of a pneumatic test is, that the steam drums can remain within the line because first we have no additional load for the bearing and only small adjustments (for the connection with the pressurisation unit and the tightening of the man ways for the applied low temperature gas test) have to be done to make the drum ready for a pneumatic loading. The pressurised air is available in every paper mill and even if the maximum pressure does not fit, the use of a compressor or pressure bottles produce no problems. 

It is important to realize that the preceding treatment is the limiting one for sufficiently small tubes and that significant departures from the limiting Eq. II-10 occur for r/a values as small as O.OS. More realistically, the situation is as shown in Fig. II-9, and the maximum pressure may not be reached until is considerably greater than 90°. 

A method for calculating the dimensions of the cavities and narrow necks from the intrusion-extrusion curves has been proposed by Reverberi." " The method is essentially as follows the ascending curve (penetration) branch is measured in the usual way, but the descending curve is mapped out from a series of steps each step commences at the same maximum pressure, proceeds to a pre-determined minimum pressure which is different for... 

The term essentially a drag coefficient for the dust cake particles, should be a function of the median particle size and particle size distribution, the particle shape, and the packing density. Experimental data are the only reflable source for predicting cake resistance to flow. Bag filters are often selected for some desired maximum pressure drop (500—1750 Pa = 3.75-13 mm Hg) and the cleaning interval is then set to limit pressure drop to a chosen maximum value. 

The characteristics of a pressed compact are influenced by the characteristics of the powder rate and manner of pressure appHcation, maximum pressure appHed and for what period of time, shape of die cavity, temperature during compaction, additives such as lubricants and alloy agents, and die material and surface condition. The effect of various compaction variables on the pressed compact are shown in Figure 6. 

Booster Pump. Use of a centrifugal booster pump avoids a low intake pressure, particularly for large, high volume units. A low pressure (>26.6 kPa (200 mm Hg)) on the iatake of a timing pump can cause vaporization of the product. The booster pump is ia the circuit ahead of the timing pump and operates only when the FDV is ia forward flow, the metering pump is ia operation, and the pasteurized product is at least 7 kPa (1 psi) above the maximum pressure developed by the booster pump (Fig. 8). 

The diameter of the air core varies with the feed volumetric flow rate. If the rate is too low, there is no air core and all of the pulp leaves the cyclone as underflow if the rate is too high, the air core expands, closing off the apex and forcing all of the pulp to leave the cyclone as overflow. Consequently there is a minimum and maximum volumetric feed rate. Because the pressure drop is proportional to the square of the volumetric feed rate, the minimum and maximum rates can be monitored by the pressure drop. The ratio of the maximum pressure drop to the minimum pressure drop should be less than 4, meaning the maximum to minimum volumetric feed rate should be less than 2. 

The equipment in which the dust is handled or stored should be designed to contain the pressure resulting from an internal explosion. Most dusts show maximum pressures of ca 345—700 kPa (50—100 psi) however, the rate of pressure rise changes from ca 700 to 70,000 kPa/s (100—10,000 psi/s). Equipment-containment design can be coupled with explosive-venting design for the equipment and the building. 

The pressure and the density of a gas are related by an equation of state. If the maximum pressure permitted within the centrifuge bowl is not too high, the equation of state for an ideal gas will suffice. The relationship between the pressure and density of an ideal gas is given by the weU-known equation ... 

Water Hammer When hquid flowing in a pipe is suddenly decelerated to zero velocity by a fast-closing valve, a pressure wave propagates upstream to the pipe inlet, where it is reflected a pounding of the hne commonly known as water hammer is often produced. For an instantaneous flow stoppage of a truly incompressible fluid in an inelastic pipe, the pressure rise would be infinite. Finite compressibility of the flmd and elasticity of the pipe limit the pressure rise to a finite value. The Joukowstd formula gives the maximum pressure... 

Example 10 Response to Instantaneous Valve Closing Compute the wave speed and maximum pressure rise for instantaneous valve closing, with an initial velocity of 2,0 m/s, in a 4-in Schedule 40 steel pipe with elastic modulus 207 X 10 Pa, Repeat for a plastic pipe of the same dimensions, with E = 1.4 X 10 Pa. The liquid is water with P = 2.2 X 10 Pa and p = 1,000 kg/m. For the steel pipe, D = 102,3 mm, b = 6,02 mm, and the wave speed is... 

The maximum pressure surge is obtained when the valve closes in less time than the period T required for the pressure wave to travel from the valve to the pipe inlet and back, a total distance of 2L. 

Typical methods are those of F. C. Zevnik and R. L. Buchanan [Chem. Eng. Progi , 59, 70-77 (Feb. 1963)] and J. H. Taylor Eng. 6-Proc. Econ., 2, 259-267, 1977). The former is mainly a graphical method of estimating the cost per functional unit (Cp) based on the capacity, the maximum pressure, the maximum temperature, and the materials of construction. The Taylor method requires the determination of the costliness index, which is dependent on the complexity of the process. A simpler method was suggested by S. R. Timms (M.Phil. thesis, Aston University, England, 1980) to give the battery hmits cost for gas phase processes only in U.S. dollars with a Marshall and Swift index of 1000. The simple equation is... 

Anchors for Expansion Joints Anchors (such as those of the corrugated, omega, disk, or shp type) shall be designed to withstand the algebraic sum of the forces at the maximum pressure and temperature at which the joint is to be used. These forces are ... 

Pressure thrust, which is the product of the effective thrust area times the maximum pressure to which the joint will be subjected during normal operation. (For shp joints the effective thrust area shall be computed by using the outside diameter of the pipe. For corrugated, omega, or disk-type joints, the effective thrust area shall be that area recommended by the joint manufacturer. If this information is unobtainable, the effective area shall be computed by using the maximum inside diameter of the expansion-joint bellows.)... 

If the test pressure as so defined would produce a stress in excess of the yield strength at test temperature, the test pressure may be reduced to the maximum pressure that will not exceed the yield strength at test temperature. 

Pipe-hue pumping stations usually range from 16 to 160 km (10 to 100 miles) apart, with maximum pressures up to 6900 kPa (1000 Ibf/ in") and velocities up to 3 m/s (10 ft/s) for liquid. Gas pipe lines have higher velocities and may have greater spacing of stations. 

Pressure-relief-device requirements are defined in Subsec. A. Set point and maximum pressure during relief are defined according to the service, the cause of overpressure, and the number of relief devices. Safety, safety relief, relief valves, rupture disk, breaking pin, and rules on tolerances for the reheving point are given. 

Filter presses are made in plate sizes from 10 by 10 cm (4 by 4 in) to 1.5 by 1.8 m (61 by 71 in). Frame thickness ranges from 0.3 to 20 cm (0.125 to 8 in). Operating pressures up to 689 kPa (100 psig) are common, with some presses designed for 6.9 MPa (1000 psig). Some metal units have cored plates for steam or refrigerant. Maximum pressure for wood or plastic frames is 410 to 480 kPa (60 to 70 psig). 

Roll presses provide a mechanical advantage in amphfying the feed pressure Pq to some maximum value P, . This maximum pressure... 

Small variations in feed properties can have a pronounced effect on maximum pressure P, and press performance. RoU presses are scaled on the basis of constant maximum pressure. The required roll loading increases approximately with the square root of increasing roll diameter or gap width. 

Peak deflagration pressure in closed equipment is approximately eight times the initial absolute pressure, whetner atmospheric, subatmo-spheric, or elevated. This maximum pressure occurs at a concentration just slightly richer in fuel than the stoichiometric concentration for combustion in air icA as shown in Table 26-14 for propane and methane ... 

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