Angular deflection

Coriolis-Type Flow Meters. In CorioHs-type flow meters the fluid passes through a flow tube being electromechanically vibrated at its natural frequency. The fluid is first accelerated as it moves toward the point of peak vibration ampHtude and is then decelerated as it moves from the point of peak ampHtude. This creates a force on the inlet side of the tube in resistance to the acceleration and an opposite force on the outlet side resisting the deceleration. The result of these forces is an angular deflection or twisting of the flow tube that is directly proportional to the mass flow rate through the tube. 

Vitrified-Clay Sewer Pipe This pipe is resistant to very dilute chemicals except hydrofluoric acid and is produced as standard-strength and extra-strength (ASTM C700). It is used for sewage, industrial waste, and storm water at atmospheric pressure. Elbows, Y branches, tees, reducers, and increasers are available. Assembly is by poured joints which allow for ample angular deflection. Joint com-... 

There are a number of features that all couplings have in common. One is the need for a spacer. API 671 calls for an 18-inch spacer minimum, This is reasonable for smaller units, say to 5,000 hp however, as the size of train increases to 15,000 to 20,000 hp, a 24-inch spacer should be considered. Above that size, longer spacers, 30 to 36 inches, are in order. The spacer first of all provides for unit separation and maintenance space. Secondly, the longer the spacer, the less the angular deflection of the coupling at its flexure point for a given offset. This makes absolute equipment alignment less critical. 

Figure 9-17. Typical plot of torsional angular deflection.

A uniform steel bar 3 ft long and 2.5 in. in diameter is subjected to a torque of 800 ft-lb. What will be the maximum torsional stress and the angular deflection between the two ends ... 

Two other features of the classical mechanics are illustrated in Fig. 3. The first is that the torque responsible for the angular deflection at low k comes from points close to r = 0 in the scaled form of Eq. (2), around which the quartic term can be ignored. Thus... 

Grooved joints resist axial forces tending to separate the joints. Angular deflection, up to the limit specified by the manufacturer, may be used to absorb thermal expansion and to permit the piping to be laid on uneven ground. Grooved joints provide quick and easy assembly and disassembly when compared with flanges, but may require more support than welded joints. 

The maximum angular deflection of the torsional ballistic pendulum is a measure of the momentum of the gases and particles emitted by the sample primer. The deflec-... 

With one end of a straight strip fixed, the other end deflects in direct proportion to the temperature change and the square of the length, and inversely as Lhe thickness, throughout the linear portion of Lhe deflection characteristic curve. Tf a strip of bimetal is wound into a helix or spiral and one end is fixed, the other end will rotate when heat is applied. The angular deflection varies directly with the temperature change and the length of the strip, and inversely with the thickness of the material, over the linear parts of the deflection characteristic curve. Bimetals show uniform deflection only over part of the deflection characteristic curve, as shown in Fig. 1. The three types of elements most commonly used in thermometers are shown in Fig. 2. 

The spherical or semi-ball joint is shown in Fig. 2.6 which includes one type of special clamp for holding the two halves of the joint together. This connection cannot freeze or stick (as conical joints sometimes do) and it introduces a degree of flexibility into the apparatus in which it is used. The area of contact between the ground surfaces is relatively small so the joints are not intended to provide for considerable angular deflection. The main application is in conjunction with conical joints rather than as a substitute for them. The conical-spherical adapters shown in Fig. 2.7 provide a means of inserting a spherical joint while retaining the conical joint principle. 

Second, an alternative hat-curved-cosine-squared potential (HC-CS) model is also considered, which, as it seems, is more adeuate than the HC-HO model. The CS potential is assumed to govern angular deflections of H-bonded rigid dipole from equilibrium H-bond direction. The HC-CS model agrees very well with the experimental spectra of water. 

The depth of any reasonable potential well should of course be finite. Moreover, the recorded spectrum of such an important liquid as water comprises two absorption bands One, rather narrow, is placed near the frequency 200 cm, and another, wide and intense band, is situated around the frequency 500 or 700 cm-1, for heavy or ordinary water, respectively. In view of the rules (56) and (57), such an effect can arise due to dipoles reorientation of two types, each being characterized by its maximum angular deflection from the equilibrium orientation of a dipole moment.20 The simplest geometrically model potential satisfying this condition is the rectangular potential with finite well depth, entitled hat-flat (HF), since its form resembles a hat. We shall demonstrate in Section VII that the HF model could be used for a qualitative description of wideband spectra recorded in water21 and in a nonassociated liquid. 

Let 0 be angular deflection of a dipole from the symmetry axis of the potential 1/(0), let p be a small angular half-width of the well (p Ci/2), and let (/0 be the well depth its reduced value u Uo/(kgT) is assumed to be 1. Since in any microscopically small volume a dipole moment of a fluid is assumed to be zero, we consider that two such wells with oppositely directed symmetry axes arise in the interval [0 < 0 < 2ji]. For brevity we consider now a quarter-arc of the circle. The bottom of the potential well is flat at 0 < 0 parabolic dependence U on 0. The form factor/is defined as the ratio of this flat-part width to the whole width of the well. Thus, the assumed potential profile is given by... 

The CS well has the form Ucs = (1 — cos2 0), where 0 is angular deflection of a dipole from the symmetry axis. The steepness p = y/Ucs/kff) of this potential, just as in Ref. 190, was chosen equal to 1.7. 

We see from Fig. 57b that if the transverse deflection c is small, the potential (20) has also a flat bottom similar to that calculated for the potential (443) at a small angular deflection p. As shown in Fig. 57b at q > 0.25, the function (443) rapidly increases. In view of Fig. 58d and Table XXI the estimated mean frequency (v) of transverse vibrations is about order of magnitude less than a mean rotational frequency. This result roughly justifies our neglect of the translational motion in derivations of the formulas for rotational motion. 

Figure 58. Density distributions of angular deflections P (a), internal-rotation frequencies (b), transverse librations (c), and their frequencies (d). Solid, dashed, and dashed-and-dotted curves refer to the H-bond length /, — 1.42,1.54, and 1.85 A. Water H2O at T — 3(X) K.

Figure 60. Effect of stretching and bending of H-bond on rotational dynamics of H20 molecule. Solid lines account for the effect of the full torque, and dashed lines account for the effect of only the stretching, (a) Reduced potential u versus angular deflection p. (b,c) Distributions of amplitudes P0 (b) and a (c). (d) Distribution of restricted-rotation frequencies vstr. (e) The dependence of the RR frequency vstr on amplitude P0. k = 6000dyn cm-1, T = 300K, Cq = 0.1, r = 1.02 A.

As usual, r is determined by the moment of inertia I of an effective linear molecule, q = Jl/ 2k-%T). Starting from the second equation in (452) and assuming that the angular deflection (3 is rather small ( 2 1), we shall give... 

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