Fluid flow mechanical energy

In a planar turbine configuration, the flow expands radially through circumferential rows of blades. Stator blade rows are fixed and tend to deviate the flow in the tangential direction. The swirling flow then enters the next blade row that is attached to the disk, the rotor. The curved rotor blades turn the flow in the opposite direction, which imparts a reaction force on the rotor. With respect to the center of the disk, this force is a moment, or torque T, that sets the rotor in motion. This process of fluid-to-mechanical energy conversion is best described by the conservation of angular momentum applied to a control volume enclosing a blade row ... 

In practice, the loss term AF is usually not deterrnined by detailed examination of the flow field. Instead, the momentum and mass balances are employed to determine the pressure and velocity changes these are substituted into the mechanical energy equation and AFis deterrnined by difference. Eor the sudden expansion of a turbulent fluid depicted in Eigure 21b, which deflvers no work to the surroundings, appHcation of equations 49, 60, and 68 yields... 

Example 3 Venturi Flowmeter An incompressible fluid flows through the venturi flowmeter in Fig. 6-7. An equation is needed to relate the flow rate Q to the pressure drop measured by the manometer. This problem can he solved using the mechanical energy balance. In a well-made venturi, viscous losses are neghgihle, the pressure drop is entirely the result of acceleration into the throat, and the flow rate predicted neglecting losses is quite accurate. The inlet area is A and the throat area is a. 

Most induction ac motors are fixed-speed. However, a large number of motor applications would benefit if the motor speed could be adjusted to match process requirements. Motor speed controls are the devices which, when properly applied, can tap most of the potential energy savings in motor systems. Motor speed controls are particularly attractive in applications where there is variable fluid flow. In many centrifugal pump, fan, and compressor applications mechanical power grows roughly with the cube of the fluid flow. To move 80 percent of the nominal flow only half of the power is required. Centrifugal loads are therefore excellent candidates for motor speed control. Other loads that may benefit from the use of motor speed controls include conveyers, traction drives, winders, machine tools and robotics. 

Clearly, the maximum degree of simplification of the problem is achieved by using the greatest possible number of fundamentals since each yields a simultaneous equation of its own. In certain problems, force may be used as a fundamental in addition to mass, length, and time, provided that at no stage in the problem is force defined in terms of mass and acceleration. In heat transfer problems, temperature is usually an additional fundamental, and heat can also be used as a fundamental provided it is not defined in terms of mass and temperature and provided that the equivalence of mechanical and thermal energy is not utilised. Considerable experience is needed in the proper use of dimensional analysis, and its application in a number of areas of fluid flow and heat transfer is seen in the relevant chapters of this Volume. 

A capillary system is said to be in a steady-state equilibrium position when the capillary forces are equal to the hydrostatic pressure force (Levich 1962). The heating of the capillary walls leads to a disturbance of the equilibrium and to a displacement of the meniscus, causing the liquid-vapor interface location to change as compared to an unheated wall. This process causes pressure differences due to capillarity and the hydrostatic pressures exiting the flow, which in turn causes the meniscus to return to the initial position. In order to realize the above-mentioned process in a continuous manner it is necessary to carry out continual heat transfer from the capillary walls to the liquid. In this case the position of the interface surface is invariable and the fluid flow is stationary. From the thermodynamical point of view the process in a heated capillary is similar to a process in a heat engine, which transforms heat into mechanical energy. 

The Department of Energy (DOE) Fundamentals Handbooks consist of ten academic subjects, which include Mathematics Classical Physics Thermodynamics, Heat Transfer, and Fluid Flow Instrumentation and Control Electrical Science Material Science Mechanical Science Chemistry Engineering Symbology, Prints, and Drawings and Nuclear Physics and Reactor Theory. The handbooks are provided as an aid to DOE nuclear facility contractors. 

A mechanical energy balance describes the various energy forms associated with flowing fluids ... 

A storage tank is shown in Figure 4-5. A hole develops at a height hL below the fluid level. The flow of liquid through this hole is represented by the mechanical energy balance (Equation 4-1) and the incompressible assumption, as shown in Equation 4-2. 

A sound understanding of the physical conservation laws is essential to one s ability to specialize them, solve them, and apply the results successfully. Therefore we begin with a derivation of the laws that govern the conservation of mass, momentum, thermal energy, and chemical species. We approach the derivation from a fluid-mechanical point of view, and the reader may find considerable overlap with other books in viscous fluid mechanics. However, we depart from the traditional presentation in two ways. First, because we are principally concerned with chemically reacting flow, we retain many features that may be negligible in fluid flow alone. Second, because we are often concerned with axisymmetric flows, we cast much of the mathematics in cylindrical coordinates rather than cartesian coordinates. While the later choice adds some complexity, it also serves to highlight some important issues that can be overlooked in cartesian coordinates. 

Frictional dissipation of mechanical energy can result in significant heating of fluids, particularly for very viscous liquids in small channels. Under adiabatic conditions, the bulk liquid temperature rise is given by AT=AP/CV p for incompressible flow through a channel of constant cross-sectional area. For flow of polymers, this amounts to about 4°C per 10 MPa pressure drop, while for hydrocarbon liquids it is about... 

For a forced vortex with spiral flow, energy is put into the fluid in the case of a pump and extracted from it in the case of a turbine. In the limiting case of zero flow, when all path lines become concentric circles, energy input from some external source is still necessary for any real fluid in order to maintain the rotation. Thus a forced vortex is characterized by a transfer of mechanical energy from an external source and a consequent variation of H as a function of the radius from the axis of rotation. 

Mechanical Energy Balance Equation. Assuming no heat transfer to or from the surroundings (q = 0) and that frictional losses end up being dissipated as heat, the Steady Flow Energy Equation for a constant density fluid becomes ... 

External forces applied to tissues lead to stretching of collagen, elastic fibers, and smooth muscle in the associated ECMs as well as proteoglycan deformation and fluid flow from within the matrix. The application of these forces ultimately leads to matrix remodeling and energy storage. The question arises as to how external mechanical events trigger cellular synthesis. 

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