Two vats are connected by a submerged pipe with a square cross-section, as shown in Figure Q2. A hinged valve in the centre of the square pipe prevents the fluid in both vats mixing. The valve door is square and has a cross sectional area 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. a) The fluid in vat 1 exerts a horizontal force, F1, on the valve door when it is closed. Express F1 in terms of h1. b) 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 terns of h1. c) Considering the fluid in both vat 1 and vat 2, express the net moment on the door in terms of h1 and h2 when it is closed.
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Q. Two vats are connected by a submerged pipe with a square cross-section, as shown in Figure Q2. A hinged valve in the centre of the square pipe prevents the fluid in both vats mixing. The valve door is square and has a cross sectional area 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.
a) The fluid in vat 1 exerts a horizontal force, F1, on the valve door when it is closed. Express F1 in terms of h1.
b) 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 terns of h1.
c) Considering the fluid in both vat 1 and vat 2, express the net moment on the door in terms of h1 and h2 when it is closed.
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