Question

Hydrostatic Force Question 1: Consider a trough, 1 meter long, whose cross-section is a semicircle of radius 2 meters. If the trough is completely filled with water (weight density 9800 N/m^3), what is the total hydrostatic force exerted on one of the semi-circular walls?

Answer 1

yt oy im. -2m, K-2m = 2n Quastia (1)>> Blonde Hydrostatic force F-fw.dly)Lys)dy (4) when w= = pg = weight-density=98000/m? To dys-depth of the fluid at y Llys = Horizontal length aty. semi-circle radius 6) = 2m. thus eqn is a xty2 = 12 se vez?gº=(2) ~4 y zo dly) = (1-4) LY from eqne) 2²42_133² * x² = 4y2, 1px = 492) xin egn (3) the value of Now, -(5) 4(8) 72% fetting Hydrostatic force.com Thus, Hydrostatic force F = 81 9800 11-4, 2J (4-43 Idy F = $229800 [4-ys → p=519600 [ Ja-Y3J - Y 14-985] dy the consen > F= 19600 [ { VA-yay ay - f g Jays dy] -66) Let I1 = { JA gazdy and Let I 2 = Now from eq (1) I, = 82 J14-yz dy (7) SALI- Sin24 det y = 2sinu So, 1 = saya ke J4-(2Simu)? Jdu afisa =2J14-92 all the values of w, dly) & LIY in ean of Now, o » J 4 y dy O (7) So ly VA-ya ay (8) 2/2 Coruldu S.. Cosu= St-sinu 72A Cas24 du => 1

172 .م = 7 TIT -19) -(19) Let th= (49) + 1, - 1. 124.6824 du = 4 Soz (14 cos2u] du => 1, - 4x * S*(1+6824)du :costu Italing > I = 2/12 (1+ Coszuldu = 2 cit Consultes > 2 [u+ 0) { Johnsrudu =} » D; = 2(12) Nos from ean (6)7 B2 = { [y J (A_ya, Jdy - (8) 27 du=-2gdy → Ydy=(-du e 22-go - u du =-ft-t du -ft- The du = 1 tu du ** = (411* **** Lysay. 12= $(14)%] => [(64)'2] = $ [8] = $ [8] = %= = 863-L) Meng day ean (6) Hydrostatic force. F= 19600 [1 ja yg dy - 1² y J14-y dy > F=1196001 - 1960013-14-3] 7 F=19600 (0.475] > F= 2310 N] Ang + J 3 of Total Hydrostatic force exerted on one the semi-chcular walls.