Two vats are connected by a submerged pipe with a square cross-section, as shown in the image attached. A hinged valve in the centre of the square pipe prevents the fluid in both vats from mixing. The valve door is square and has a cross sectional area of L X L, and the hinge is at the top of the door. The fluid depth in the first tank is h1 and the depth in the second tank is h2. The fluid in Vat 1 exerts a horizontal force, F1, on the valve door when it is closed. Express F1 in terms of h1. The fluid in Vat 1 exerts a Moment M1 on the valve door (acting about the hinge at the top of the door) when it is closed. Express M1 in terms of h1. Considering the fluid in both vat1 and vat2, express the net moment on the door in terms of h1 and h2 when it is closed. If the valve can withstand a moment of Mmax before opening, find the maximum possible height difference between the fluid in vats 1 and 2.
Two vats are connected by a submerged pipe with a square cross-section, as shown in the image attached. A hinged valve in the centre of the square pipe prevents the fluid in both vats from mixing. The valve door is square and has a cross sectional area of L X L, and the hinge is at the top of the door. The fluid depth in the first tank is h1 and the depth in the second tank is h2.
The fluid in Vat 1 exerts a horizontal force, F1, on the valve door when it is closed. Express F1 in terms of h1.
The fluid in Vat 1 exerts a Moment M1 on the valve door (acting about the hinge at the top of the door) when it is closed. Express M1 in terms of h1.
Considering the fluid in both vat1 and vat2, express the net moment on the door in terms of h1 and h2 when it is closed.
If the valve can withstand a moment of Mmax before opening, find the maximum possible height difference between the fluid in vats 1 and 2.
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