Flow measurements perfect fluid

In any case, the fluid temperature at the wall is different from that at the centerline of the flow. When the fluid is being heated, the wall temperature is higher than the centerline temperature, and vice versa for cooling the fluid. The bulk or mixing cup temperature of the fluid, T, is the temperature that would be measured if the total flow through a cross section were collected over a given period and perfectly mixed. The bulk temperature is intermediate between the wall temperature and the centerline temperature (but usually close to the latter) and is the temperature that... 

What physical meaning should one attach to the velocity potential For the flow of an ideal, frictionless fluid, the velocity potential has no physical meaning whatever. To illustrate this, consider the steady flow of a frictionless, constant-density fluid in a horizontal pipe see Fig. 10.3. (Such a frictionless fluid, once started in motion by some external force, would continue moving forever, because there is no force to stop it.) For such a frictionless fluid, the velocity is uniform over the cross section perpendicular to the flow. From Bernoulli s equation we can see that there is no change with distance of pressure, velocity, or elevation, and by straightforward arguments we can show that there is no change of temperature, refractive index, dielectric constant, or any other measurable property. But from Eq. 10.7 we know that, because is constant, there is a steady decrease of (f> in the x direction. Thus the velocity potential for a perfect fluid (f> is not a function of any measurable physical property of the fluid. 

Now that we have found the perfect-fluid solution for the pressure at various points on the surface of a cylinder, we must inquire whether nature really behaves this way Figure 10.18 shows the pressure at various values of 6 calculated from Eq. 10.67 as well as the measured pressures at the same angles at two different flow rates. For both flow rates there is fair agreement between the observed pressures and Eq. 10.67 along the front of the cylinder (0 to 90 and 270 to 360 ), but there is very poor agreement for the back of the cylinder. The explanation is in terms of separation, described next. 

The RTD in a system is a measure of the degree to which fluid elements mix. In an ideal plug flow reactor, there is no mixing, while in a perfect mixer, the elements of different ages are uniformly mixed. A real process fluid is neither a macrofluid nor a microfluid, but tends toward one or the other of these extremes. Fluid mixing in a vessel, as reviewed in Chapter 7, is a complex process and can be analyzed on both macroscopic and microscopic scales. In a non-ideal system, there are irregularities that account for the fluid mixing of different... 

An extension of case 4.4-l(l) is demonstrated in Fig.4.4-1(2). The scheme comprises of a plug flow reactor, a feeding reactor 1 and a collector 4, as before. In addition, measurement points of the concentration, simulated by small perfectly mixed reactors 2 and 3, were added. The residence time of the fluid in the plug flow reactor is tp. These reactors make it possible to include the recycle stream Q32, impossible to add in case 4.4-l(l). Reactors 2 and 3 simulate also reactors 2 and 11 in example 4.4-1. 

Thermal conductivity (k) n. The basic measure of steady heat-transfer rate within solid materials (and still fluids) by atomic or molecular contact and vibration. It derives from Fourier s law of heat conduction and may be thought of as the rate of heat flow between two opposite faces of a unit cube whose other faces are perfectly insulated when the temperature at the warmer face is 1 K above that of the cooler face. The SI dimensions corresponding to this concept are (J/S)/(m K/m), which reduces to W/m K. Some conversions from other units to SI are given in the Appendix. For plastics and other materials, k increases with rising temperature. Tide DR (ed) (2004) CRC Handbook of chemistry and physics. CRC Press, Boca Raton, EL. Ready RG (1996) Thermodynamics. Pleum Publishing Company, New York. Seanor DA (1982) Electrical conduction in polymers. Academic Press, New York. 

The question arises as to whether or not irreversible processes exist in the framework proposed. The answer is affirmative for real systems. Every measuring system involves certain errors even if the measuring system is perfect, it uses a certain amount of energy in the measurement process itsel f. For example, consider a viscous fluid which is flowing in a channel. It is difficult to measure the temperature distribution at all positions in the fluid, since an inherent energy conversion process occurs from a mechanical form to heat due to viscous dissipation in the fluid (cf. Sect. 3.4.4). Thus a certain amount of heat energy can be omitted even though it exists in the fluid. This results in an apparent irreversible process, which can be accounted for in our framework. 

The methods that are usually used to calibrate ultra small-volume fluids are the static weighing method, comparing method, flow veloeity measurement method, and so on. The study of picoliter flows has just begun, so the perfect calibration methods have not been formed yet. This section will review partial methods to produce pL flow, their measurement accuracy and the relevant calibration methods. A fuller coverage is not possible because of space limitations. 

RTD methods are based on the concept of age distribution functions and make use of the experimentally measured or calculated residence time distribution of fluid elements in a reactor vessel (Figure 12.3-1, C and D). A Lagrangian perspective is taken and the age of a fluid element is defined as the time elapsed since it entered the reactor. In what follows, steady state operation of a vessel fed with a volumetric flow rate F is considered. A residence time distribution (RTD) experiment can be performed with inert tracers, such that at an instant of time all fluid elements entering a reactor or process vessel are marked. The injection of an impulse of tracer into the vessel at time zero can be mathematically represented by means of the Dirac delta function or perfect unit impulse function ... 

F(t) is a probability distribution which can be obtained directly from measurements of the system s response in the outflow to a step-up tracer input in the inflow. Consider that at time t = 0 we start introducing a red dye at the entrance of the vessel into a steady flow rate Q of white carrier fluid. The concentration of the red dye in the inlet flow is C. At the outlet we monitor the concentration of the red dye, C(t . If our system is closed, i.e. if every molecule of dye can have only one entry and exit from the system (which is equivalent to asserting that input and output occur by convection only), then QC(t)/QCQ is the residence time distribution of the dye. This is evident since all molecules of the dye appearing at the exit at time t must have entered into the system between time 0 and time t and hence have residence times less than t. Only if our red dye is a perfect tracer, i.e.. if it behaves identically to the white carrier fluid, then we have also obtained the residence time distribution for the carrier fluid and F(t) = C(t)/C. To prove that the tracer behaves ideally and that the F curve is obtained, the experiment should be repeated at different levels of C. The ratio C(t)/C at a given time should be invariant to C, i.e. the tracer response and tracer input must be linearly related. If this is not the case, then C(t)/CQ is only the step response for the tracer, which includes some nonlinear effects of tracer interactions in the system, and which does not represent the true residence time distribution for the system. 

---