Question

4. Consider the rectangular gates shown Figure 4. They are both the same size, but Gate A is held in place by a horizontal shaft through its midpoint and the other is cantilevered to a shaft at its top. Compute the torque (moment) required to hold the two gates closed. Comment on how the required torques change as H is increased Shaft Gate A Shaft Water Gate B H Water h pheric Atmospheric h pressure Atm pressure Figure 4

Answer 1

two conditions Cate and CraB) need to Codeuelate the +orque gien Solutions We have of to hold the wo ates closed aUso them we 1or both requisred to ind toraue So wt wit taut with ffrt gate we hawe uquired wates tevel (Et ffect ef sufeing the Unate A Susface frree P. Catm) foree aering gease mfreeusface presune goomree busface let, F at centre of Preuee C. be the pherure hm alepth of centrold Cntre Depth of Depth of botom end (D) of gate fnree furface Heright gake 17 width of gate Presswe ore gate due to diquid actog Premune forces on 17 On rentre pressue Rekultant au &tep: Ne have helalfon Ahene force 01 4otel Az AMEA of gte cent re fprenue +5 AF

bh3 12 Plate is rectangulas Qnd h AB +80 9O 프 unit 2 AB (H-h unit umsts (bhi)/12 2 b2 2 12 H-h 2. (M-h) 2 +12 12 2 4 (4-2) 12 2 12HH +3 h h+ 1242- .12 i fo4 h 122-124h H-) 12 3H2-3Hh 24-3 (4-5) 2 4- A3(2 H h2+34(H-h) 3 (241 Il

PRep.T Torque hequire to Keep the gateclbsed wf be CA X OC b2+ 3H (H-h) .- 3 (2H- No

14- 2 2 CA 17 35 4- 2 CA N2 243H 3Hh 2 48- LA 3h2 SA TA 4h2-3h2 2 This fs the dequired toraue at we need to apply to keep the gate 12 closed the valeie of wi fncreave the tequtred torqyue oill not hawe Ony change ince Ca only depends on as 4

For trateB Since in this case hinge fs at top end of gate S0, we oft 4ake the moment oebouut point BI h appited fENeed to be a Nao Toraue eauined oftt be T=FxBC Prom Step 4/ + Case BC gate PM-A3)4+ +3H 3 (4 47 34h SHh-62 Hh +h2 h*+9uh-3-3 2 3h 4 3Hh-h COcwhon : m equaiton that we Aay the value Can nequired wlu Pnerease as Anerease
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