Exam Review 8.6, ER 10 Bio-mimetic gel was used in the study of genetics and ult

Question

Exam Review 8.6, ER 10 Bio-mimetic gel was used in the study of genetics and ultimately banded by the Federation. A Ferengi transport ship is carrying a 5-centimeter [cm] radius cylindrical tank of bio-mimetic gel to sell on the black market. A hydrostatic pressure probe located at the bottom of the tank reads 60 millimeters of mercury [mm Hg]. If the specific gravity of the gel is 8.9, what is the mass of gel contained in the tank in units of kilograms [kg]? Assume acceleration due to gravity simulated on the Ferengi vessel to be 8.4 meters per second squared [m/s 2]. Thinking Like an Engineer Stephan, Bowman, Park, Si Oniand An Active Leaning Approach Copyright 2018 Pearson Prentice-Hall, Inc. 4m Edition

Explanation / Answer

Pressure noted = 60 mm of Hg =13560 *8.4*0.06 = 6834.24 Pa

Specific gravity of gel = 8.9

Density of gel = 8900 kg/m3

Height of gel to have pressure of 6834.24 Pa = 6834.24/(8900*8.4)=0.091 m

radius of tank = 5 cm=0.05m

Volume of gel = pi*0.052*0.091 = 7.147*10-4 m3

Mass of gel = 8900*7.147*10-4 = 6.36 kg

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