Momentum, rate change

The above example shows the effect of a change in pipe diameter, and therefore flow area, on the momentum flow rate. It is clear that for steady, fully developed, incompressible flow in a pipe of constant diameter, the fluid s momentum must remain constant. However, it is possible for the fluid s momentum to change even in a straight pipe of constant diameter. If the (incompressible) flow were accelerating, as during the starting of flow, the momentum flow rates into and out of the section would be equal but there would be an accumulation of momentum within the section. (The mass of fluid in the section would remain constant but its velocity would be increasing.) Consequently, a force must act on the fluid in the direction of flow. 

Conservation of Mass. The law of conservation of mass for a compressible medium is usually expressed in an Eulerian framework as, "the time rate change of mass density at any point is equal to the negative divergence of the momentum density at that point."... 

Product feed rate It s important to know that product feed rates and feed rate changes are sometimes used to control finished product moistures. Weigh belts are common for powdered products, and there is a wide variety of equipment available for liquid feeds. Momentum devices are inexpensive but less accurate. 

Includes the effects of skin friction and the change in the momentum rates in the entrance region (developing flows)... 

The strategy for solving fluid dynamics problems begins by putting a control volume within the fluid that matches the symmetry of the macroscopic boundaries, and balancing the forces that act on the system. The system is defined as the fluid that is contained within the control volume V, which is completely surrounded by surface S. Since a force is synonymous with the time rate of change of momentum as prescribed by Newton s laws of motion, the terms in the force balance are best viewed as momentum rate processes. The force balance for an open system is stated without proof as l = 2- -3H-4- -5, where... 

The value of the apparent friction factor can be calculated by means of Eq. 13 if the total pressure drop from z = 0 to z is known. The apparent value of the friction factor takes into account both the skin friction and the change in momentum rate due to change in the shape of the velocity profile in the hydrodynamic entrance region (see Fig. 1). 

The external force should equal the time rate change in momentum,... 

The rate of change of momentum of a fluid can be expressed as a product of mass flow rate change in velocity... 

Momentum Flow Meters. Momentum flow meters operate by superimposing on a normal fluid motion a perpendicular velocity vector of known magnitude thus changing the fluid momentum. The force required to balance this change in momentum can be shown to be proportional to the fluid density and velocity, the mass-flow rate. 

The starting point for obtaining quantitative descriptions of flow phenomena is Newton s second law, which states that the vector sum of forces acting on a body equals the rate of change of momentum of the body. This force balance can be made in many different ways. It may be appHed over a body of finite size or over each infinitesimal portion of the body. It may be utilized in a coordinate system moving with the body (the so-called Lagrangian viewpoint) or in a fixed coordinate system (the Eulerian viewpoint). Described herein is derivation of the equations of motion from the Eulerian viewpoint using the Cartesian coordinate system. The equations in other coordinate systems are described in standard references (1,2). 

The rate of change of momentum equals the sum of the forces on a fluid particle (Newton s second law). 

It is possible to determine the x-component of the momentum equation by setting the rate of change of x-momentum of the fluid particle equal to the total force in the x-direction on the element due to surface stresses plus the rate of increase of x-momentum due to sources, which gives ... 

MOMEN- TUM BALANCE Rate of change of momentum per unit volume Rale of change of momenium by convection per unit volume Rale of change of momentum by molecular transfer (viscous transfer) per volume Generation per volume (External forces) (Ex gravity) Empirically determined flux specified (3)< Velocity specified (1.2b) ... 

Consider a nucleus with magnetic moment pi in a magnetic field Ho- According to classical mechanics the rate of change of the angular momentum G is the torque T. 

Regardless of type, overall fan action must depend on a rate of change of gas momentum in a tangential direction. Without this change in momentum, no resisting torque can exist, and no fan power input is required or absorbed. ... 

Conservation of Momentum. If the mass of a body or system of bodies remains constant, then Newton s second law can be interpreted as a balance between force and the time rate of change of momentum, momentum being a vector quantity defined as the product of the velocity of a body and its mass. 

That influence on a body that causes it to accelerate. Quantitatively, it is a vector equal to the body s time rate of change of momentum. 

Since in real fluids, some of the energy of fluid flow is typically converted into heat by viscous forces, it is convenient to generalize equation 9.7 so that it allows for dissipation. Consider the momentum of fluid flowing through the volume dT (= pv). Since its time rate of change is given by d pv)/dt = dp/dt)v -f p dv/dt), we can use equations 9.3 and 9.7 to rewrite this expression as follows ... 

Observables, rate of change of, 477 Occupation number operator, 54 for particles of momentum k, 505 One-antiparticle state, 540 One-dimensional antiferromagnetic Kronig-Penney problem, 747 One-negaton states, 659 One-particle processes Green s function for computing amplitudes under vacuum conditions, 619... 

Rate of change of observables, 477 Ray in Hilbert space, 427 Rayleigh quotient, 69 Reduction from functional to algebraic form, 97 Regula fold method, 80 Reifien, B., 212 Relative motion of particles, 4 Relative velocity coordinate system and gas coordinate system, 10 Relativistic invariance of quantum electrodynamics, 669 Relativistic particle relation between energy and momentum, 496 Relativistic quantum mechanics, 484 Relaxation interval, 385 method of, 62 oscillations, 383 asymptotic theory, 388 discontinuous theory, 385 Reliability, 284... 

By accelerating the gaseous combustion products through the exhaust nozzle, a thrust is imparted to the nozzle and motor case. This thrust is determined by the time rate-of-change of the total momentum of the bounded fluid, as indicated by the expression... 

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