Work done by fluid

In our problem the work done by fluid (w) and pump work on fluid (q) are zero. 

The nonconvective energy flux across the boundary is composed of two terms a heat flux and a work term. The work term in turn is composed of two terms useful work deflvered outside the fluid, and work done by the fluid inside the control volume B on fluid outside the control volume B, the so-called flow work. The latter may be evaluated by imagining a differential surface moving with the fluid which at time 2ero coincides with a differential element of the surface, S. During the time dt the differential surface sweeps out a volume V cosdSdt and does work on the fluid outside at a rate of PV cos dS. The total flow work done on the fluid outside B by the fluid inside B is... 

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-... 

The equation that expresses conservation of energy can also be determined by considering Fig. 2.3. Since the piston moves a distance u At, the work done by the piston on the fluid during this time interval is Pu At. The mass of material accelerated by the shock wave to a velocity u is PqU At. The kinetic energy acquired by this mass element is therefore (pqUu ) At/2. If the specific internal energies of the undisturbed and shocked material are denoted by Eq and E, respectively, the increase in internal energy is ( — o)Po V At per unit mass. The work performed on the system is equal to the sum of kinetic and... 

Over the time increment dt, the force applied on the left-hand side of the element acts over a distance u dt, so the work done on the element from the left is Pu dt. The force on the right-hand boundary of the element k P + (dPIdh), dh, and it travels a distance (u + (dufdh), dh) dt, so the work done by the element on the surrounding fluid to the right is (P + (dP/dh), dh)(u + (dujdh), dh) dt. The net work done on the fluid element is the difference... 

Wiedermatm (1986b) presents an alternative method for calculating work done by a fluid. The method uses the lambda model to describe isentropic expansion, and permits work to be expressed as a function of initial conditions and only one fluid parameter, lambda. Unfortunately, this parameter is known for very few fluids. 

The work done by an expanding fluid is defined as the difference in internal energy between the fluid s initial and final states. Most thermodynamic tables and graphs do not presentbut only h, p, v, T (the absolute temperature), and s (the specific entropy). Therefore, u must be calculated with the following equation ... 

The specific work done by an expanding fluid is defined as. 

The specific work done by a fluid in expansion is calculated with Eq. (6.3.25) as follows ... 

The speciflc work done by the fluid in expansion can be read from Figures 6.30 or 6.31 if its temperature is unknown. Saturated propane at a pressure of 1.9 MPa (19 bar) has a temperature of 328 K, almost the superheat-limit temperature. Note that it is assumed that temperature is uniform, which is not necessarily the case. From Figure 6.30, the expansion work per unit mass for saturated liquid propane is... 

W = work done by a system against its surroundings, Btu/lb or Btu Z = height from center of gravity of a fluid mass to a fixed base level, ft... 

The graphical representation of work done by an expanding fluid as an area is due initially to James Watt, who applied it to the indication of steam engines it was generalised and introduced as a very convenient aid to thermodynamical reasoning by E. Clapeyron in 1834. 

If the fluid flows from section 1 to section 2 (where the values of the various quantities are denoted by suffixes 1 and 2 respectively) and q is the net heat absorbed from the surroundings and W, is the net work done by the fluid on the surroundings, other than that done by the fluid in entering or leaving the section under consideration, then ... 

The work done by the pump is found by setting up an energy balance equation. If W, is the shaft work done by unit mass of fluid on the surroundings, then —Ws is the shaft work done on the fluid by the pump. 

That is, the net energy or work put into the fluid by the pump goes to increasing the fluid pressure or the equivalent pump head, Hp. However, because pumps are not 100% efficient, some of the energy delivered front the motor to the pump is dissipated or lost due to friction. It is very difficult to separately characterize this friction loss, so it is accounted for by the pump efficiency, rje, which is the ratio of the useful work (or hydraulic work) done by the pump on the fluid (—w) to the work put into the pump by the motor (—wm) ... 

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 ([/). 

Note that we call this term positive when work is done on the system, just as we make Q positive when heat is removed from the reactor. Thus the signs on Wj and Q are opposite to those of dq and dw, in the thermodynamic equations. We are always interested in shaft work done by a stirrer on the reactor fluid, and we are usually interested in cooling rather than heating. Therefore, we carry these sign conventions so that we can be sure of the signs of these terms. 

Figure 3.2. The work done by the expansion of a fluid for different conditions.

In many cases Eq. (10.5) is greatly shortened owing to the fact that certain quantities are equal and thus cancel each other or are zero. Thus, if two points are at the same elevation, zi x2 = 0. If the conduit is well insulated or if the temperature of the fluid and that of its surroundings are practically the same, q may be taken as zero. On the other hand, q may be very large, as in the case of flow of water through a boiler tube. If there is no machine between sections (1) and (2) of Fig. 10.1, then the termM drops out. If there is a machine present, the work done by or upon it may be determined by solving Eq. (10.5) for M. 

It seems reasonable to assume that similar temperature profiles will also exist when viscous dissipation is important. Attention will first be given to the adiabatic wall case. If the wall is adiabatic and viscous dissipation is neglected, then the solution to the energy equation will be T = Ti everywhere in die flow. However, when viscous dissipation effects are important, the work done by the viscous forces leads to a rise in fluid temperature in the fluid. This temperature will be related to the kinetic energy of the fluid in the freestream flow, i.e., will be related to u /2cp. For this reason, the similarity profiles in the adiabatic wall case when viscous dissipation is important are assumed to have the form ... 

---