Final velocity

The final velocity of these two ions will be the same, but their final flight times will differ by the above turnaround time, This results in a broadening of the TOF distributions for each ion mass, and is anotiier limiting factor when considering the mass (time) resolution of the instrument. 

The kinetic or translational energy of the ions is equal to the work done on moving the charged species through the potential, V, i.e., l/2mjVi = zV and l/2m2V2 = zV, where z is the charge on the ions and Vj, V2 are their final velocities. From this, we obtain Equations 33.1 and 33.2. 

The left term of Equation 2.80 represents a head drop required to accelerate the flow from an initial velocity to the final velocity V2. If the initial velocity is low it can be assumed negligible and if density p = I.A is substituted into Equation 2.80, it can be written as... 

In some convection equations, such as for turbulent pipe flow, a special correction factor is used. This factor relates to the heat transfer conditions at the flow inlet, where the flow has not reached its final velocity distribution and the boundary layer is not fully developed. In this region the heat transfer rate is better than at the region of fully developed flow. 

Throttling The expansion of a fluid through a constricted passage (across which there is a pressure difference), during which no external work is done. The initial and final velocities of the fluid are equal, and there is no heat exchange with external sources. A change in entropy will, however, take place. 

If a collision is purely plastic, then the two colliding bodies will adhere to each other and move on as a single body. Knowing the initial velocities and masses thus allows calculation of the final velocity. 

In this case, an additional equation is required before the final velocities may be found. Thus, the coefficient of restitution e is defined as the ratio of the velocity of separation to the velocity of approach ... 

Sphere I weighs 1 lb and is traveling at 2 ft/s in the positive x direction when it strikes sphere 2, weighing 5 lb and traveling in the negative x direction at 1 ft/s. What will be the final velocity of the system if the collision is (a) plastic, or (b) Elastoplaslic with e = 0.5 ... 

If a single particle is falling freely under gravity in an infinitely dilute suspension, it will accelerate until it reaches a steady-state velocity. This final velocity is known as the terminal settling velocity (t/t) and represents the maximum useful superficial velocity achievable in a fluidised bed. Thus, the contained particles will be elutriated from the column if the superficial velocity is above Ut, the value of which can be predicted using the Stokes equation... 

Let the initial velocities of the particles be v2 and v3, and their final velocities be vi and v the initial and final relative velocities will be... 

From these relations between the initial and final velocities of each of the particles, it follows that the jacobian of the transformation is unify, so that... 

Inverse Collisions.—The particle velocities resulting from a collision between particles of velocities vx and v2, having collision parameters 6 and e, have been denoted as v[ and v they may be found from Eqs. (1-21). Consider now the particle velocities resulting from a collision between particles of velocities v[ and v2, with collision parameters b and e let these final velocities be denoted by v[ and v . 

Nonlinearity of the coefficient of heat conductivity results in the new physi- cal effects, the main of which is a final velocity of heat conducting. In what S... 

The Bernoulli effect—In a rapidly expanding flow, the two phases accelerate differently. For low initial velocities, the ratio of final velocities at the end of expansion, Va/VL, can be approximated by (pL/pG)u2-... 

In examination of Pentolite, the following values were determined Plexiglas gap, Time to detonation, Distance to detonation, Final velocity in Plexiglas and Initial velocity in acceptor. For example, for gap 0.798 inches, Time to detonation 2.5 /tfiec, Distance 8.8 mm, Final vel in Plexiglas 3.8 mm/psec, Initial vel in acceptor was 3.4 mm/nsec. Other values were 0.812 in,... 

The gas stream from the inlet system (Fig. 2.2) enters the ionization chamber (operated at a pressure of about 10-6 — 10"5 torr) in which it is bombarded at right angles by an electron beam emitted from a hot filament. Positive ions produced by interaction with the electron beam are forced through the first accelerating slit by a weak electrostatic field. A strong electrostatic field then accelerates the ions to their final velocities. To obtain a spectrum, the applied magnetic field is increased, bringing successively heavier ions into the collector slit. A scan from mass (strictly m/z see above) 12 — 500 may be performed in seconds. 

For a collision (which we will arbitrarily label 1) the directions of initial and final velocities are given by the unit vectors t>i and t>2- The scattering... 

We consider the non-LTE spectral formation in a spherically expanding atmosphere. The velocity field v(r) is specified in its supersonic part by the usual analytical law with the parameters y, (final velocity) and the exponent 8=1, The temperature structure is derived from the assumption of radiative equilibrium, but only approximately evaluated for the grey LTE case. The atmosphere is assumed to consist of pure helium. The model atom has a total of 28 energy levels, among these 17 levels of He I. The line radiation transfer is treated in the "comoving frame". 

M 14] [P 14] Video-image analysis of the droplet displacement shows that an S-shaped dependence over time is yielded, i.e. the initial and final velocities are low, having the highest velocity after an induction period for the moving droplet [98],... 

The equations governing the amount of sand transported superficially are easily derived. Let V be the velocity with which a particle rises after impact by another saltating particle and 2 its final velocity after it has traveled a distance x downstream. Since u2 is very large as compared with vu the amount of momentum lost in saltation per unit length of path by a mass of sand q of unit width is... 

Solution This is a steady-flow process for which Eq. (2.10h) applies. The initial and final velocities of water in the storage tanks are negligible, and the term bu2/2gc may be omitted. The remaining terms are expressed in units of (Btu)(lbnl) 1 through use of appropriate conversion factors. At 200(°F) the density of water is 60.1 (lbm)(ft)-3, and l(ft)3 is equivalent to 7.48(gal) thus the mass flow rate is... 

Air expands through a nozzle from a negligible initial velocity to a final velocity of 350ms What is the temperature drop of the air, if air is assumed an ideal gas for which CP = (7/2)/ ... 

Example 2.7 Air at 1 bar and 25°C enters a compressor at low velocity, discharges at 3 bar, and enters a nozzle in which it expands to a final velocity of 600 m at the initial conditions of pressure and temperature. If the work of compression is 240 kJ per kilogram of air, how much heat must be removed during compression ... 

One notes that in this theory the energy transfer is treated classically and thus no allowance is made for the effect of a quantum jump on the final velocity of the impinging molecule. 

The entrance loss he, in feet, assuming a basket-type strainer is used at the suction-pipe inlet, is Kv2/(2g), where K = a constant from Fig. 6.14 v = liquid velocity, in ft/s and g = 32.2 ft/s2. The exit loss occurs when the liquid passes through a sudden enlargement, as from a pipe to a tank. Where the area of the tank is large, causing a final velocity that is zero, hex = v2/lg. 

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