The Carmen-Kozeny equation is used to calculate the head loss through a sand filter. The images below show a spreadsheet designed to calculate this head loss. Reproduce the spreadsheet as shown. Create the equation as shown below, and also use subscripts and superscripts in the cells as depicted. You are also to name cells B20 through B24, and use the names in all appropriate formulae. In addition, protect all cells from being changed except those cells with blue text. The percent smaller column is calculated as: 100 - sum of the percent retained. The Reynolds number (Re) and friction factor (f) are calculated by formulae shown in the worksheet below. The fx/d column is the ratio of the product of the friction factor and the percent retained to the mean diameter. The head loss cell is calculated from the Carmen-Kozeny equation as given in the spreadsheet below. Be careful when calculating the results; particularly pay attention to your units. You may (or may not) recall from your fluids class that 1ft³ = 7.48 gallons and that the gravitational constant in US customary units is 32.17 ft/s²; I'll just leave those there for you. You should also note that the sand diameter uses a notation that is common in engineering texts: the diameter has units of ft x 103. This means a value of 3 in the table should be interpreted as 3 x 10-3 ft. Use the following names for the parameters in the formula for Reynolds number and head loss: Parameter Shape factor Porosity Name shape Porosity Kinematic viscosity KinVisc Bed depth Bed Depth Va (gpm/ft2) approachV Va (ft/s) vel (See the next page of this assignment for the format of the completed spreadsheet) 3 4 The Carmen-Kozeny equation is 5 6 7 h₁ 8 9 10 where ht 11 12 13 g 14 fi Upon completion, your spreadsheet should appear as follows: A B 1 Headloss through a sand filter C D E 2 This problem is a modification of Sample Problem 4.1 in Reynold's Text e Va L(1-e) V² fix 3 eg headloss porosity F Friction factor f=150 (1-e) +1.75 d₁ Re Reynolds Number V d Re = a approach velocity gravity friction factor G H J v 15 Xi weight fraction 16 di 17 L avg particle diameter bed depth where $ shape factor Pw density of water 18 V kinematic viscosity 19 Parameter Table 20 Shape Factor: 1 21 Porosity: 0.42 Kinematic 22 Viscosity (ft²/s): 0.0000141 23 Bed Depth (ft): 3 24 Va (gpm/ft²): 2.5 25 Va (ft/sec) 0.00557041 26 27 Geometric Mean 28 Sieve Size Sand Diameter Percent Percent Reynolds f fx/d 29 Pass-Retain ft x 10³ Retained Smaller Number 30 14-20 3.283 2.8 97.2 1.297 68.83 587 31 20-28 2.333 7.5 89.7 32 28-32 1.779 35 ཀླུ#⌘863ཥྞཐཱབབ་ 33 32-35 1.500 46 59 54.7 8.7 35-42 1.258 4.8 3.9 35 42-48 1.058 3.1 0.8 48-60 0.888 0.4 0.4 60-65 0.750 0.2 0.2 65-100 0.583 0.2 ~~~98420 0.922 96.14 3,091 0.703 125.54 24,698 0.593 148.56 45,559 0.497 176.80 6,746 0.418 209.89 6,150 0.351 249.74 1,125 0.296 295.37 788 0 0.230 379.48 1,302 39 sum 100 90,045 Headloss, ft 2.04