Resistance to flow in pipes

Friction Head This is the pressure required to overcome the resistance to flow in pipe and fittings. It is dealt with in detail in Sec. 5. 

The fluid must not exceed a definite maximum viscosity at the lowest ambient temperature so that the pump can induct the fluid under an ambient of, say, 4 inches of mercury (46,000-foot altitude), and the resistance to flow in the pipes be kept sufficiently low. 

Elastic properties usually have a negligible effect on resistance to flow in straight pipes, but examples have been noted that the resistances of fittings may be as much as 10 times as great for viscoelastic liquids as for Newtonian ones. 

Circulation rate through the reboiler is fixed by the driving force and the resistance to flow. In a fixed piping system, it is a function of the liquid level in the reboiler sump in the case of natural circulation, and of pump design and operation in the case of forced circulation. 

Resistance to flow in the valves, regenerators, and associated piping affects the efficiency of the cycle adversely only to the extent that the cold space is not fully pressurized and depressurized. In this event, the heat load is less than the ideal p - pq)v by approximately Ap + Apq ) K, where Ap is the pressure deficit at the end of the filling stroke and Apq is the excess at the end of the depressurization. The exact analysis is very complicated and requires consideration of the effect of inactive volume as well as modified regenerator performance. 

To apply these data and equations to the problem of ground resistance, the maximum anticipated current must first be estimated. For practical industrial situations, Iq varies in the range 0.01-100/rA. The upper value represents extreme cases such as microfiltration and the lower value to slow flow in pipe. Typical charging currents for tank tmck loading are of the order 1 /rA (5-3.1.1). As an example, consider a system such as a tank with a capacitance less than 1000 pF. First, consider the minimum ignition voltages in Table A-4-1.3b. From Eq. (2), f L = In the case of hydrogen the mini-... 

The resistance to flow through the various piping components that make up the. system (except vessels, tanks, pumps—items which do not necessarily provide frictional resistance to flow) such as valves, fittings, and connections into or out of equipment (not the loss through the equipment) are established by test and presented in the published literature, but do vary depending on the investigator. 

In general, pardally due to the size and cost of maintaining vacuum in a piping system, the lines are not long (certainly not transmissions lines), and there is a minimum of valves, fittings, and bends to keep tire resistance to flow low. 

As the air or gas flows through the blower system (piping/ ducts, filters, etc.), the movement causes friction between the flowing air/gas. This friction translates into resistance to flow, whether on the inlet (suction side) or outlet (discharge side) of the system in which the blower is a part and that creates the pressure drop (see Chapter 2, V. 1, 3 Ed., of this series) which the blower must overcome in order for the air/gas to move or flow. This resistance to flow becomes greater as the velocity of flow increases, and more energy or power is required to perform the required flow movement at the required pressures. 

When a fluid is flowing through a pipe, resistance to flow is caused by friction. The pipe bore selected for each section must be such that under any operating conditions, the initial head, either static head of oil in the supply tank or the pump delivery pressure, will be adequate to ensure the required flow rate. Additionally, any change of flow rate and consequent variation in loss of head must not adversely affect the operation of the associated oil-burning equipment. 

Resistance to flow. The coating should show no tendency to flow from the pipe under prevailing climatic conditions. It must not melt or sag in the sun and it must have sufficient resistance not to be displaced from the underside of large-diameter pipes. 

A loss coefficient can be defined for any element that offers resistance to flow (i.e., in which energy is dissipated), such as a length of conduit, a valve, a pipe fitting, a contraction, or an expansion. The total friction loss can thus be expressed in terms of the sum of the losses in each element, i.e., ef = JT K-nVf/7). This will be discussed further in Chapter 6. 

A special condition called slack flow can occur when the gravitational driving force exceeds the full pipe friction loss, such as when a liquid is being pumped up and down over hilly terrain. Consider the situation shown in Fig. 7-5, in which the pump upstream provides the driving force to move the liquid up the hill at a flow rate of Q. Since gravity works against the flow on the uphill side and aids the flow on the downhill side, the job of the pump is to get the fluid to the top of the hill. The minimum pressure is at point 2 at the top of the hill, and the flow rate (Q) is determined by the balance between the pump head (Hp = — w/g) and the frictional and gravitational resistance to flow on the uphill side (i.e., the Bernoulli equation applied from point 1 to point 2) ... 

However, this expression assumes that the total resistance to flow is due to the shear deformation of the fluid, as in a uniform pipe. In reality the resistance is a result of both shear and stretching (extensional) deformation as the fluid moves through the nonuniform converging-diverging flow cross section within the pores. The stretching resistance is the product of the extension (stretch) rate and the extensional viscosity. The extension rate in porous media is of the same order as the shear rate, and the extensional viscosity for a Newtonian fluid is three times the shear viscosity. Thus, in practice a value of 150-180 instead of 72 is in closer agreement with observations at low Reynolds numbers, i.e.,... 

A major complication, especially for separated flows, arises from the effect of slip. Slip occurs because the less dense and less viscous phase exhibits a lower resistance to flow, as well as expansion and acceleration of the gas phase as the pressure drops. The result is an increase in the local holdup of the more dense phase within the pipe (phase density, pm), as given by Eq. (15-11). A large number of expressions and correlations for the holdup or (equivalent) slip ratio have appeared in the literature, and the one deduced by Lockhart and Martinelli is shown in Fig. 15-7. Many of these slip models can be summarized in terms of a general equation of the form... 

The conductance value C is the flow volume through a piping element. The equation (1.11) could be thought of as Ohm s law for vacuum technology , in which qpy corresponds to current, Ap the voltage and C the electrical conductance value. Analogous to Ohm s law in the science of electricity, the resistance to flow... 

Ideal fluids are those in which there is no loss of energy due to friction, there are no interactions between the molecules that make up the fluid, and there are no interactions between the fluid molecules and the pipe, tubing, or container. In everyday life we deal with real fluids not ideal fluids. Viscosity is a measure of a fluid s resistance to flow. Fluids with high viscosity such as honey do not flow very readily, while fluids with low viscosity such as water flow more easily. Let s take a closer look at a real fluid flowing through a horizontal pipe of length L and cross-sectional area A, as shown in Figure 5.12. 

The same is true for fluid flow in piping. Experimental data must first be established to solve the piping fluid flow problems, specifically the / factor, also called the hL factor in the Fig. 6.1 analogy. Please note also that / is dimensionless. The / factor is used later in this chapter. The hL factor is in units of feet it is a force, requiring a workload, which is the force of friction resisting fluid flow. This friction of resistance is on the internal wall surface of the pipe. 

The variable D is the pipe internal diameter in feet. This variable sets the internal surface area for friction resistance to flow and the internal cross-section area flow parameters. A common usage of D is making the equivalent pipe length to diameter ratio L ID for valves and fittings ... 

C In one stage of a process for the manufacture of liquid air, air as a gas at 4 atm abs and 250K is passed through a long, insulated 3-in. ID pipe in which the pressure drops 3 psi because of frictional resistance to flow. Near the end of the line, the air is expanded through a valve to 2 atm abs. State all assumptions. 

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