Acceleration of free fall

V is the velocity of sedimentation and a is the acceleration of free fall or centrifugation. 

Fig. 23. Pressure drop and flooding correlation for various random packings (95). ip = p- o IP-l (standard acceleration of free fall) = 9.81 m/s, p, = liquid viscosity ia mPa-s numbers on lines represent pressure drop, mm H2O /m of packed height to convert to ia. H2O /ft multiply by 0.012. Packing...

We want to find the relation between the height, h, of the column of mercury in a barometer and the atmospheric pressure, P. Suppose the cross-sectional area of the column is A. The volume of mercury in the column is the height of the cylinder times this area, V = bA. The mass, ttt, of this volume of mercury is the product of mercury s density, d, and the volume so m = dV = dhA. The mercury is pulled down by the force of gravity and the total force that its mass exerts at its base is the product of the mass and the acceleration of free fall (the acceleration due to gravity), g F = mg. Therefore, the pressure at the base of the column, the force divided by the area, is... 

This pressure can also be reported as 101 kPa, where 1 kPa = 103 Pa. The acceleration of free fall varies over the surface of the Earth and depends on the altitude in all calculations in this text, we assume that g has the standard value used here. 

The height, h, of a column of liquid in a capillary tube can be estimated by using h = lylgdr, where y is the surface tension, d is the density of the liquid, g is the acceleration of free fall, and r is the radius of the tube. Which will rise higher in a tube that is 0.15 mm in diameter at 25°C, water or ethanol The density of water is 0.997 g-cm-3 and that of ethanol is 0.79 g-cm-3. See Table 5.3. 

FIGURE 834 The pressure at the base of a column of fluid is equal to the product of the acceleration of free fall, g, the density, d, of the liquid, and the height, h, of the column. 

In some cases, it may be necessary to calculate the osmotic pressure from the height, h, of the solution (in an apparatus like that in Fig. 8.31) by using 11 = gdh, where d is the density of the solution and g is the acceleration of free fall (see inside back cover). 

The force with which a body or entity is attracted to earth. The weight, W, is equal to the product of the mass, m, of the body and the acceleration of free fall in a vacuum (Le., W = mg). Since the earth is not a perfect sphere of uniform density, the weight of a body varies at various locales on the earth s surface. In practice, the mass of a body is determined by comparing its weight with a set of known standards Le., milm2 = W1IW2. 

Example. If initial horizontal velocity is 30 m/s, and initial vertical velocity is 30 m/s, calculate the distance that the volcanic bomb can go. The standard acceleration of free fall is 9.8 m/s. ... 

To estimate how high water will rise in a vertical tube of internal radius 2.0 mm at room temperature, we take the surface tension of water from Table 5.3 and insert if in the expression for h in Eq. 6 the acceleration of free fall is given inside the back cover, and the density of water is 1.0 g-cm-3, corresponding to 1.0 X 103 kg-m 3. Recall that 1 N = 1 kg-m-s-2. Then... 

Self-Test 6.1A Calculate the work needed for a person of mass 65 kg to go between the two floors of a house, a difference in height of 3.5 m. The difference in potential energy of the person will be mgh, where m is the mass, g is the acceleration of free fall (9.81 m-s 2), and h is the height climbed. 

In the definition, v is the velocity of sedimentation and a is the acceleration of free fall or centrifugation. The symbol for a limiting sedimentation coefficient is [s], for a reduced sedimentation coefficient 5°, and for a reduced limiting sedimentation coefficient [s°] see [l.e] for further details. 

The following symbols are used in the definitions of the dimensionless quantities mass (m), time (t), volume (V area (A density (p), speed (u), length (/), viscosity (rj), pressure (p), acceleration of free fall (p), cubic expansion coefficient (a), temperature (T surface tension (y), speed of sound (c), mean free path (X), frequency (/), thermal diffusivity (a), coefficient of heat transfer (/i), thermal conductivity (/c), specific heat capacity at constant pressure (cp), diffusion coefficient (D), mole fraction (x), mass transfer coefficient (fcd), permeability (p), electric conductivity (k and magnetic flux density ( B) ... 

Fig. 23. Pressure drop and flooding correlation for various random packings (95). V = 0 /Pl> (standard acceleration of free fall) = 9.81 m/s2,...

For V we substitute Stokes law v = 2a Apg/9rj (see (1.6.4.331) where a is the particle radius, Ap the density difference between particle and solution and g the standard acceleration of free fall or the corresponding acceleration caused by centrifugation. Electrophoretic retardation Is Ignored and Q = 4ne ea., as for the Coulomb case. We obtain... 

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