(Solved): A pressurized tank contains oil \( (s=0.9) \) and has a triangular gate of negligible weight, as il ...

A pressurized tank contains oil \( (s=0.9) \) and has a triangular gate of negligible weight, as illustrated below. Compute the magnitude of force \( \vec{F} \) so that the gate remains closed as shown. Note: Since the gate is non-rectangular, you should perform the above problem using the general approach, however you cannot use \[ F=\gamma h_{c} A \text { nor } y_{p}=y_{c}+I_{x x . c} / A y_{c} \] because these equations were \( d \) rrived while taking pressure equal to zero at the liquid surface. Meanwhile in this problem pressure is not equal to zero at the surface of the oil. Thus, looking back at the week \( 8 / \) part 1 lecture notes posted on Canvas, you should re-derive the expressions for \( F \) and \( y_{p} \) valid for non-zero pressure at the surface.