Question

3.93 Determine the minimum volume of concrete (g = 23.6 kN/m3) needed to keep the gate (1 m wide) in a closed position, with l = 2 m. Note the hinge at the bottom of the gate. 1/4 Stop Submerged concrete block Water Hinge

Answer 1

wine the minimum volume of caucrete 19-2 headed to keep the gate, heith el=am. Note the ne 23.6KNIM Keep the gate (Im wide) in a closed position, m . Note the linge at the bottom of the gate. soli Since, specifle were Now , We have lce, specifle weight of weight density of a thing is the ratio between the height of fiuld to it's volume. se W = Weight of fluid mass of fuild yg S volume of fluid volum of fuuld w apg {where og is acch due to goeivity} gor we = 23.6 kN/m3 ş specific weight of ? concrete as We} width of the gate, b= lm (Giren) length of the gate , &= 2m ( Given) Now , Force acting on the gåte, Feate = Ww (he) (bl) { where Was is ? specific weight of putting the value of each term in above expression, lale get Egede 9.81 ( 2) (1 mx 2m) = 19.62 KN weiter?

Now, I, To To cal calculate the centre of pressure Note: Centre of pressure is the depth point poter i is the depth point of 1. application of total pressure forte a h IG +AKIG I Ah Ah ди. Whose IG a moment of inertia of red about axis passing through the G. G of area and parallel to free Surface of liquid . ħ = Distance CG of the dred from face Surface Of Ciguid. A = Total Area of Surface Subtituting the hillue alle get 42 *s (212 = 12(T ža 1 :0.33 CZ -osom 2)

Mow, for calculating the weight of gffe Algate = Fgate ( al - ht) E 19.62 KNG 2 – 0.33) 2m + 2m 19.62 KN 1 1m-0.33m) 2m + / m 13.1454 2.5m Maw W = 5.258 KN for volume of concrete weight of gate 5.258 KN < = 23.6 kN/m3–9.51 km lang We - Ww 5.258 KN 13.79 KNIm3 TV = 0.3812 m3 ans