The following data were generated from the normal Use the

Use Newton’s viscosity law to determine the shear stress τ Nm 2 at the surface y = 0, τ = µ du d y Assume a value of dynamic viscosity µ = 1.8 × 10 −5 N · sm 2 . y , m 0.002 0.006 0.012 0.018 0.024 u , ms 0.287 0.899 1.915 3.048 4.299

21.22 Fick’s first diffusion law

states that Mass ux = −D dc d x P21.22 where mass flux = the quantity of mass that passes across a unit area per unit time gcm 2 s, D = a diffusion coefficient cm 2 s, c = concentration gcm 3 , and x = distance cm. An environmental engineer measures the following con- centration of a pollutant in the pore waters of sediments un- derlying a lake x = 0 at the sediment-water interface and increases downward: x , cm 1 3 c , 10 − 6 gcm 3 0.06 0.32 0.6 Use the best numerical differentiation technique available to estimate the derivative at x = 0. Employ this estimate in conjunction with Eq. P21.22 to compute the mass flux of pollutant out of the sediments and into the overlying waters D = 1.52 × 10 −6 cm 2 s. For a lake with 3.6 × 10 6 m 2 of sediments, how much pollutant would be transported into the lake over a year’s time? 21.23 The following data were collected when a large oil tanker was loading: t , min 10 20 30 45 60 75 V , 10 6 barrels 0.4 0.7 0.77 0.88 1.05 1.17 1.35 Calculate the flow rate Q i.e., dVdt for each time to the order of h 2 . 21.24 Fourier’s law is used routinely by architectural engi- neers to determine heat flow through walls. The following temperatures are measured from the surface x = 0 into a stone wall: x , m 0.08 0.16 T , °C 19 17 15 If the flux at x = 0 is 60 Wm 2 , compute k. 21.25 The horizontal surface area A s m 2 of a lake at a par- ticular depth can be computed from volume by differentiation: A s z = d V d z z where V = volume m 3 and z = depth m as measured from the surface down to the bottom. The average concen- tration of a substance that varies with depth, ¯c gm 3 , can be computed by integration: ¯c = Z cz A s z d z Z A s z d z where Z = the total depth m. Determine the average con- centration based on the following data: z , m 4 8 12 16 V , 10 6 m 3 9.8175 5.1051 1.9635 0.3927 0.0000 c , gm 3 10.2 8.5 7.4 5.2 4.1 21.26 Faraday’s law characterizes the voltage drop across an inductor as V L = L di dt where V L = voltage drop V, L = inductance in henrys; 1 H = 1 V · sA, i = current A, and t = time s. Deter- mine the voltage drop as a function of time from the follow- ing data for an inductance of 4 H. t 0.1 0.2 0.3 0.5 0.7 i 0.16 0.32 0.56 0.84 2.0 21.27 Based on Faraday’s law Prob. 21.26, use the follow- ing voltage data to estimate the inductance if a current of 2 A is passed through the inductor over 400 milliseconds. t , ms 0 10 20 40 60 80 120 180 280 400 V , volts 0 18 29 44 49 46 35 26 15 7 21.28 The rate of cooling of a body Fig. P21.28 can be ex- pressed as d T dt = −kT − T a where T = temperature of the body °C, T a = temperature of the surrounding medium °C, and k = a proportionality con- stant per minute. Thus, this equation called Newton’s law of cooling specifies that the rate of cooling is proportional to