There are three Fluid Mechanics problems attached. Please guys i need to solve them?

Question

Robert · Accepted Answer

SOLUTIONS 1
Figure shows the forces acting on gate  
FX   = Pressure force acting on gate side AO 
FY   = Pressure force acting on gate side AB 
RX and RY = Reaction forces on hinge at O 
hcx= Vertical distance of centre of gate side AO from water surface  
hcx= 3+2 = 5 m 
hcy= Vertical distance of centre of gate side AB from water surface  
hcy= 3+4= 7 m 
Area 
 AAO = 4X3=12 m
2 
AAB = 2x3= 6 m
2 
As we know for water  
Kg/m3 
FX   = x g x hcx x AAO 
FX   = 1000 x 9.8 x 5 x 12 
FX 
FY 
RX 
RY 
P 
FX   = 588000 N 
FX   = 5.88 x 10
5 N 
Similarly  
FY   = 1000 x 9.8 x 7 x 6 
FY   = 4.116 x 10
5 N 
Now we will take moment about hinge O 
First we calculate the location of FX 
hRx = [ I / (hcx x AAO) ] + hcx  
I = (1/12) x 3 x 43 = 16 m4 
hRx = [16 / (5 x 12) ]+ 5 
hRx = 5.2666 m = 5.267 m 
∑ Mo = 0 
FX (5.267 – 3) + FY x 1 – P x 4 = 0 
FX (5.267 – 3) + FY x 1 = P x 4 
5.88 x 105 (5.267 – 3) + 4.116 x 105 = P x 4 
105 x [5.88 (5.267 – 3) + 4.116] = P x 4 
P = 4.361 x 105 N = 436.1 KN 
P = 436 KN 
Answer  
P = 436 KN

There are three Fluid Mechanics problems attached. Please guys i need to solve them?

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