Rate of work

The first integral on the right-hand side is the rate of work done on the fluid in the control volume by forces at the boundaiy. It includes both work done by moving solid boundaries and work done at flow entrances and exits. The work done by moving solid boundaries also includes that by such surfaces as pump impellers this work is called shaft work its rate is Ws-... 

At still higher true stress, do/de, the rate of work-hardening decreases further, becoming insufficient to maintain stability - the extra stress in the neck can no longer be accommodated by the work-hardening produced by making the neck, and the neck grows faster and faster, until final fracture takes place. 

The rate of change of energy is equal to the sum of the rate of heat addition to and the rate of work done on a fluid particle (first law of diermodynamics). 

The most celebrated textual embodiment of the science of energy was Thomson and Tait s Treatise on Natural Philosophy (1867). Originally intending to treat all branches of natural philosophy, Thomson and Tait in fact produced only the first volume of the Treatise. Taking statics to be derivative from dynamics, they reinterpreted Newton s third law (action-reaction) as conservation of energy, with action viewed as rate of working. Fundamental to the new energy physics was the move to make extremum (maximum or minimum) conditions, rather than point forces, the theoretical foundation of dynamics. The tendency of an entire system to move from one place to another in the most economical way would determine the forces and motions of the various parts of the system. Variational principles (especially least action) thus played a central role in the new dynamics. 

Hydrogen is pumped from a reservoir at 2 MN/m2 pressure through a clean horizontal mild steel pipe 50 nun diameter and 500 m long. The downstream pressure is also 2 MN/m2 and the pressure of this gas is raised to 2,6 MN/m2 by a pump at the upstream end of the pipe. The conditions of flow are isothermal and die temperature of the gas is 293 K. What is the flowrate and what is the effective rate of working of the pump ... 

This is true of skeletal muscle, particularly the white fibers, where the rate of work output—and therefore the need for ATP formation—may exceed the rate at which oxygen can be taken up and utilized. Glycolysis in erythrocytes, even under aerobic conditions, always terminates in lactate, because the subsequent reactions of pymvate are mitochondrial, and erythrocytes lack mitochondria. Other tissues that normally derive much of their energy from glycolysis and produce lactate include brain, gastrointestinal tract, renal medulla, retina, and skin. The liver, kidneys, and heart usually take up... 

As before, we ignore kinetic energy and consider Equation (2.18) as a rate equation for the system separating out the rate of work due to shear and shafts, Ws, and pressure, Wv. Then... 

In this approach the energy input into the polymer fluid is modeled as the work done by the moving surface on the fluid. The rate of work (u>.) is modeled as the product of the force F) times the velocity ([/). 

In the Cartesian system used for an unwrapped screw, the rate of work can be represented in terms of the viscosity, the local velocities, and the screw geometry. 

The rate of work inputted for flow in the z direction due to motion of the core,, is as follows ... 

The dissipation is calculated for barrel rotation in the screw pump device in a similar manner. For this case, the velocities Vozl, and are used for the calculations, and they are provided by Eqs. 7.21,7.23, and 7.27, respectively. The rate of work input for barrel rotation tv, is obtained by multiplying the normal shear stress for the barrel surface by the velocity of the barrel surface integrated over the barrel surface area. The traditional method for calculation of dissipation for barrel rotation is as follows ... 

Substituting the shear stresses and velocities and then integrating provides the rate of work for the channel as Eq. 7.88 for barrel rotation. As before for screw rotation, dissipation is a positive definite quantity, and thus the absolute value of the pressure gradient is used. The dissipation between the flight lands and barrel wall is the same for barrel and screw rotation. 

Here the viscosity is combined with the pressure gradient to make the caiculations simpie. This combined method is acceptabie oniy for Newtonian fluids. The rate of work divided by the viscosity for the components is next. 

The rate of work inputted by the rotating screw, energy conducted through the bar-rei wait, and energy conducted to the screw can be accounted for in each voiume. The energies dissipated tu here are based on the flow in a singie channei and a unit iength for the surface. The caicuiation is as foiiows for the voiume for screw rotation ... 

The rate of work to the material in the flight clearance,, is the same for screw rotation and barrel rotation. The rate of work was previously provided in the literature [1] as follows ... 

For viscous dissipation, the absolute value of used. The rate of work... 

Eq. A7.165 is a negative stress. Since dissipation is always positive, the sign in Eq. A7.165 will be changed. The rate of work due to pressure-induced flow in the z direction at the core is as follows ... 

The absolute value of the pressure gradient is used to force the rate of work term to be positive. 

For viscous dissipation the absolute values of the velocity and stress will be used. The rate of work added for barrel rotation and flow in the x direction ... 

The SI unit of power or radiant flux (symbolized by W) equal to one joule per second (or, meter per kilogram per second ). With respect to electric currents, the watt is the rate of work expressed by a current of one ampere and a potential difference of one volt. See Power Radiant Flux... 

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