# Fluid Mechanics Gate Problem

1. Jan 27, 2016

### jdawg

1. The problem statement, all variables and given/known data
A rectangular plate AB is 1.8 [m] wide and 2.0 [m] long. As shown below the plate is used to keep water (blue region) confined to the region. Find the weight of the gate necessary to keep the water enclosed. Assume the hinge at A is frictionless.

2. Relevant equations

3. The attempt at a solution
I used 9810 N/m^33 for the specific weight of water.
tanθ=4/3
θ=53.13°
A=(2m)(1.8m)=3.6m2
hCG=(2m)+(1m)sin(53.13)=2.8m
FH2O=(9.807)(1.6)(3.6)=98884.8 N

Ixx=((1.8m)(2m)3)/12 =1.2m4

ycp=(-Ixx)sinθ)/(hCGA)= - 0.09508m

MA=0=(By)(2)cos(53)-W(1)cos(53)+FH2O(1)cos(53)-FH2O(1)sin(53)

I'm not really sure if I'm correct up to this point. Is my placement of theta in the free body diagram correct?
Thanks!

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Last edited: Jan 27, 2016
2. Jan 27, 2016

### SteamKing

Staff Emeritus
It's not clear from the problem statement how you know the gate has a slope of 4:3 when it is closed.