2. Choose and answer one of the following two questions [you only need to answer one of these questions}: 1. [Volmnes by CrossSections and Improper hitegrals) Gabriel's Horn is the surface obtained by revolving the curve 3; = 1," 1', :r 2 1T around the :raxis. Compute the volume of revolution enclosed by Gabriel's Horn. Gabriel's Horn 2. [Are Length) Find the length of the curve 3'; = log [cos at} between :I.' = {1' and :r = :IrftL Folkind with its aun vertical. Calivlate the spood in rev/min at china the while reached the inside edge of the lip and the total "right of worry spine the underide of the lip imet, hat vertical sides and at one place there is a right anded . the redlun of the bond at the centerling of the channd bec firemrs. If the channel he filled by s Could Dowing alogy It, thow idadity of tie fluid at radius . Show idio that for 1 = IN the gumin Bowing hoe Marvin / where A mere h the In preware bead in the bend between the le ner and outer wide of the chaand. An impeller, 0-0 mdiss rotating comempirically shout a ver. mu in f doidofaddad euler 0 9 m diani, produces worlet ciotion in the water with which the casing is completely and, Inside the Impeller, the vortex motion is forced whilst, be. to con the Impeller and the circular side of the during the vortex ls thee The pressure head at the tip of the citing is 12 m of water when the presmite head at the centre of the casing hi 1-I'm of water, Chain the speed of the impeller in revmin, Aturn 210 m/min 7 Inwed redial flow occur between two horizontal discs Ond min ciam and 75 m napart, the water leaving through a gen- toal pipe 150 min diem in the lower disc at the rate of 0-17 m /s. If the absolute pressure at the outer edge of the disc is 101 EN/me calculate the pressure at the outlet, Find also the resultant force o Dir upper dia. Two horizontal discoare 12-5 man apart and 300 ra cium, later flows racially outward, be wees the discs from 1 50 mm pope at the centre of the lower dike. If che pressure at the her edit of the clit in s mospheric, calculate the promcare in the soppy pipe when the velocity of the water in the pipe is 6 m/s. Find also the truliant pressure on the upper disc, neglecting MarHET -17-5 IN/ml, 136-7N A forged vortex 0-3 in dum is roteled at 120 rewmin and is surrounded by a free vortex of infinite rodent. Find the height of desertice s infinity above the lovel at the centre. Ammar 0-367 m A compound vorles formed in water having a free surface comprise a central Forced yonex surrounded by a free vortex. The nation belloon the velocity in my's and the radius in metres in go 10- for the forced romex and iv = 0-9 for the free vortex. Canwin the depth of the centre of the depression in the water sun foon below the free surface level