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Question 2 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 XL, 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 terms of ₁. 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.

Question 2 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 XL, 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 terms of ₁. 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.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Question 2 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 h, and the depth in the second tank is h2. a) The fluid in vat 1 exerts a horizontal force, F,, on the valve door when it is closed. Express F, in terms of h,. 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 M, in terms of h,. c) Considering the fluid in both vat 1 and vat 2, express the net moment on the door in terms of h, and h, when it is closed. d) 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. h2 h1 Figure Q2: Two vats of water connected by a hinged door.
Transcribed Image Text:Question 2 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 h, and the depth in the second tank is h2. a) The fluid in vat 1 exerts a horizontal force, F,, on the valve door when it is closed. Express F, in terms of h,. 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 M, in terms of h,. c) Considering the fluid in both vat 1 and vat 2, express the net moment on the door in terms of h, and h, when it is closed. d) 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. h2 h1 Figure Q2: Two vats of water connected by a hinged door.
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