Question

A quarter circle gate that weighs 314kg is used to keep a certain liquid inside of a tank, as shown in the image. Calculate the force in kN that the spring must generate to keep the gate in position Consider that the gate is 2.15 meters deep into or out of the screen). Consider that the properties of water are: v=0.294x10-6m²/s and p=0.285mPas. X SG = 1.3 B 1-w 5m у X = y = 2R 3(4 – 1) ΑΙ R= 1m

Answer 1

Given h sm B tu F o: R=m weight of gate AB = 314kg Density of fluid = 1300 kg/m3 = 2.15m Depth gate o Com Position of 31 ý = te alf CS Scanned with CamScanner

Let & fy are horizontal k verticle forces on the gate. Sg fr = SgAh 1300 X10 X 1X215 x ħ sl - 4 - 5 - 27 So, fr = 122 IN This auts at centre of pressure. ä ht Iu sinto " Ah el 11 4.38m fy= 8 x 2.158 lox Area S-71 Area = (SXI) - 6) = So, fy = 52 KN CS Scanned with CamScanner

3 force ad through COM of gate A - Fx Is-a ã = 0.62 A WE balance about D so Moment + Fe (0.62) F = Fy (1 - 2 - so, fa sz (1-22) + 122 (0-63) F = 94.5 KN cs Scanned with CamScanner