Frictionally resisted expansion

We may now use equation (14.12) along with equation (14.15) to yield the corresponding temperature differential for a frictionally resisted expansion from the same initial conditions (p, T) ... 

Therefore, the enthalpy change for a frictionally resisted expansion may be found by substituting from equation... 

Accordingly, the velocity for a frictionally resisted expansion trough the nozzle is given by substituting from (14.32) into (14.27) ... 

Evaluation of downstream enthalpies following isentropic and frictionally resisted expansions... 

The value of phi after a frictionally resisted expansion, B, will be found in the same temperature row as ha-Gas tables are generally more precise than steam tables because of the need to tabulate only against temperature, rather than temperature and pressure. However, interpolation may be needed to give the best possible accuracy. 

The final enthalpy following a frictionally resisted expansion is given by ... 

Bending or torsional flexibihty may be provided by bends, loops, or offsets by corrugated pipe or expansion joints of the bellows type or by other devices permitting rotational movement. These devices must be anchored or otherwise suitably connected to resist end forces from fluid pressure, frictional resistance to pipe movement, and other causes. 

Since the downstream station was chosen arbitrarily, it follows that the required relationship between specific volume for a frictionally resisted, adiabatic expansion is simply ... 

The significance of the change in polytropic exponent with efficiency is brought out more clearly if we take the mth root of both sides of equation (14.22) to restate the equation defining the frictionally resisted, adiabatic expansion in the alternative form ... 

We will now develop an expression for the sonic speed experienced in the throat/outlet of a convergent-only nozzle and at the throat of a convergent-divergent nozzle when the expansion is frictionally resisted. Sonic conditions will exist in the throat when the velocity calculated by applying equation (14.45) to the convergent section of the nozzle has reached the local speed of sound, i.e. ... 

In the real case where the expansion is frictionally resisted with efficiency, t), the actual specific enthalpy at the end of the expansion will be as given by equation (16.44) ... 

When the elastic deformation energy and the gas expansion energy released by coal burst is higher and the additional stress reaches a certain level enough to overcome the rolling frictional resistance at the top and the sliding frictional resistance at the bottom of coal seam, on the one hand, the coal was stressed and compressed further, on the other hand, the displacement towards to the low stress area (roadway coal wall) takes place, and it is shown as figure 2. 

The effect of temperature changes and shrinkage of the superstructure needs to be considered when the superstructure is rigidly connected with the supports. Where expansion bearings are used, forces caused by temperature changes are limited to the frictional resistance of the bearings. 

Hardness, thermal expansivity, thermal conductivity, tensile strength, impact strength, shear strength, coefficient of friction, resistance to water, resistance to wear, elastic modulus and machinability,... 

Expansion anchors transfer tension loads to the hase material via friction between the expansion elements of the anchor and the wall of the hole. The magnitude of the friction resistance is directly proportional to the degree of expansion force developed by the anchor. Expansion forces are produced in response to the relative movement of sloping surfaces within the anchor mechanism. The maimer in which this relative movement is produced is important for distinguishing the anchor function in response to tension loads. The two most common mechanisms for producing expansion forces are represented by displacement-controlled and torque-controlled anchors ... 

Astrom and Pipes (28) showed that (he importance of the thermal expansion is small (less than 2% in terms of the matrix pressure). The viscous resistance and compactation are the major contribution to the pulling force and the friction resistance is negligible. This is a consequence of the small magnitude of (he pressure load reached in the die so that the matrix pressure does not contribute to die pulling force. 

For wear resistance and low friction, coatings of PTFE or M0S2 generally have been satisfactory. Use of low thermal expansion filler in PTFE helps minimise cracking and loss of adhesion from metal substrates with their lower coefficients of expansion. 

The internal friction due to vortices occurs in rapid expansion, diverging, and regulation valves. The entropy generation due to those vortices is taken into consideration in the local resistance. The entropy generation is directly proportional to c- thus. 

The films are generally dark in colour and often show a fine network of cracks due to differential expansion of oxide and metal on warming to ambient temperature. They are generally left unsealed, since sealing markedly reduces abrasion resistance, but may be impregnated with silicone oils to improve the frictional properties. Applications include movable instrument parts, pump bodies and plungers, and textile bobbins. 

Polyimide It is a high-cost heat and fire resistant plastic, capable of withstanding 500°F (260° C) for long periods and up to 900°F (482° C) for limited periods without oxidation. It is highly creep resistant with good low friction properties. It has a low coefficient of expansion and is difficult to process by conventional means. It is used for critical engineering parts in aerospace, automotive and electronics components subject to high heat, and in corrosive environments. 

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