Question

Pumping a conical tank A right- circular conical tank, point down, with top radius 5 ft and height 10 ft is filled with a liquid whose weight-density is 60 lb/ft^ 3 . How much work does it take to pump the liquid to a point 2 ft above the tank? If the pump is driven by a motor rated at 275 ft-lb/sec (1/2 hp), , how long will it take to empty the tank? Must work the integral out by hand and show all steps

Pumping a conical tank A right-circular conical tank, point down, with top radius 5 ft and height 10 ft is filled with a liquid whose weight-density is 60 lb/ft?. How much work does it take to pump the liquid to a point 2 ft above the tank? If the pump is driven by a motor rated at 275 ft-lb/sec (1/2 hp), how long will it take to empty the tank? Must work the integral out by hand and show all steps.

Answer 1

Given data : The top radius of the conical tank is: R=541 The height of the comical tant is: H = loft density of the liquid ini wa = 60 lb/ft3 additional height above the tant is: D=1 The power motor isip = 275 ft. lbl sec The weighted of the The relation of height and given distance is as : R -14 h ala xh 8: A Substitute values in abone equation 54 xh 10 A b. a expresion The to the volume of the elemental section is Da 4 Tr ² (dh) VE * 6)dh I ² (dh) expresion for the of the liquid in goven as weight F = Wo v The Wy* I ha (dk)

The expression for the distance moved by the liquid ay S = H+D-h ession for the work done is given ass The expression dw = Fos dw a Wdx e bę (db) · (H+D-h) The height will vary from the distance D to the distance (D+H)... on integrating the above equation with limieto of D and CD+H), Ws * h2(dh). (H +D-h) Defl4 I dw S 0 Subotitute values in above equation • S 0 2 12 w Saw - J o war Jaw. du 60 lb) 43 * Ę xh (da) (12–1) #7.12 * S 62(du) (12-1) = 47.12 Sacrah?_he) da) 2 2+) 3+1 la ܩܝ h [w]" = 48012/18 x * [ia at1 341 2 [w] = 447.12 x [iex the chose w = -47.1* *** - ) 47012 [C4x123 - 1st ) - (4x2 ² - 2 W-0

E E 47012 (16912-5184 ) - ( 38 - 47.12 (1728 - 728 - 28) = 47.19 (1700) W = 80104 lb. ft. Thus, the work done to pump the liquid above the 2 feet of the tank in 80104 Iboft.