Viscosity and Thermal Conductivity of Water: Gaseous and liquid States.

1964

AIChE Journal

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existed during the upward movement of the impeller. When the impeller is brought sufficiently close to the bottom of the tank, the flow pattern will shift to that of a propeller and the power output will drop. Figure 1 is a typical plot of power output vs. impeller height. The existence of hysteresis, a range of impeller heights in which two power outputs exist, is clearly shown.If ,the impeller is stopped and then started, the upper curve in Figure 1 is followed irrespective of the direction in which the impeller is moved. Hysteresis exists only during continuous impeller operation. This effect has been observed at mixing Reynolds numbers of from 20 to 1,000 with the Newtonian materials listed in Table 1.The mixing-power number at the low impeller height is 15% to 20% below the power number for the standard height.This effect of hysteresis has little practical significance, since the height of an impeller in a tank is rarely, if ever, changed during a process. However, the impeller in a tank is often located near the bottom. The design engineer must take into account the reduced power and altered %ow pattern when the impeller is low, so that the equipment is designed to do a satisfactory mixing job. A reduced power output means reduced mixing, and the speed of the impeller should accordingly be increased to compensate.

Section: Viscosity Datamentioning

confidence: 99%

The viscosity of polar substances in the dense gaseous and liquid regions

Stiel

1964

AIChE Journal

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Thermal pressure applied to the prediction of viscosity of simple substances in the dense gaseous and liquid regions

Lennert

1965

AIChE Journal

The reduced thermol pressure-temperature ratio has been used to relate residual viscosity modulus for argon, krypton, and xenon into a unique relotionship applicable for the dense gaseous and liquid regions. For these monatomic substances the critical compressibility foctor i s zc = 0.291. Values of (~P R /~T R )~R vs. (fi -p*)E an log-lag coordinates produced a linear relationship. For these simple substances, this relationship was used to predict viscosities with an average deviation of 3.0% for fifty eight experimental values. This relationship was also applied for the prediction of viscosities for nitrogen, oxygen and carbon dioxide.The approach developed in this study merits further examination with several additional substances. The lack of adequate thermal pressures in the dense gaseous and liquid regions of substances other than argon limits the use of this study to substances having critical compressibility factors zc = 0.291.The effect of pressure on the viscosity of substances in the dense gaseous and liquid regions has been represented by a relationship between the residual viscosity pp" and p , the density. Experimental viscosities of gases at elevated pressures and of the liquid state have been utilized to produce individual relationships of p -pccD vs. p for argon (20), nitrogen (1 ), oxygen (1 ) , hydrogen (1 ) , carbon dioxide (lo), ammonia ( S ) , and water ( 2 3 ) , Each of these relationships was found to be continuous when extended from the gaseous state to the liquid state. Using a dimensional analysis approach, Thodos and co-workers (9, 22) have consolidated these individual relationships for polar and nonpolar substances into a single continuous curve by relating the quantity ( pp.") Q to pR, the reduced density. Water was not included because it exhibits an abnormal behavior, which may be due to its excessive hydrogen bonding effects. The viscosity parameter [ has been shown to be . $ = T,"'/M"TtP from dimensionalanalysis. The ( pp * ) Q vs. relationship is unique and exhibits a high dependence on density, especially in the liquid state. The complex nature of this function has required the use of a fourth-degree polynomial for its description over the complete range of the gaseous and liquid states (9).In view of the high dependence of ( p -EL") Q on reduced density, it would prove advantageous to introduce a thermodynamic quantity comparable to density which might provide a simpler functional relationship with ( py " ) 4, the residual viscosity modulus. THERMAL PRESSUREshow that the van der Waals' equation of state From an elementary type of treatment, it is possible to can produce the following expression: Equation (2) states that the sum of the external pressure P and the internal pressure a/v2 is equal to the quantity T ( d P / d T ) ", which, according to Hirschfelder, Curtiss, and Bird ( 7 ) , is defined as the thermal pressure.For the general case, the PVT behavior can be expressed in terms of a virial type of equation of the form (3) where B ( T ) , C ( T ) , . . . are temperature...

Thermal conductivity of simple gases at normal pressures

Roy

1968

Can J Chem Eng

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Thermal conductivity measurements available in the literature for simple gases at normal pressures (approximately 1 atmosphere) were used to obtain the product k*λ, where the parameter, λ =M1/2Tc1/6/Pc2/3. Separate relationships between k*λ and TR resulted for monatomic, diatomic and triatomic gases. The relationships for monatomic gases can be expressed as follows For the diatomic and triatomic gases, linear relationships resulted, when at the same reduced temperatures, their k*λ values were plotted against (k*λ)m on log‐log coordinates. These relationships can be expressed in equation form as follows and Thermal conductivities calculated with these relationships have been compared with experimental values and produce an average deviation of 2.8% for the monatomic gases (219 points), 4.3% for the diatomic gases (282 points) and 4.6% for the triatomic gases (242 points). In this treatment, helium and hydrogen do not follow the general pattern and consequently these substances have been treated separately.