A water gate is to be reinforced with three horizontal beams (running to the page). If the water acts on one side only to a depth of \(h = 6m\), find the positions of the beams measured from the water surface so that each beam will carry an equal load. Gate is fully covered by water.**Diagram Explanation:**The diagram shows a triangular shape representing the water gate. The height \(h\) is marked on the left-hand side, indicating the total depth of the water, which is given as 6 meters. Three horizontal beams are depicted along the vertical side of the triangle, each with distances \(d_1\), \(d_2\), and \(d_3\) from the water surface downwards.The centroid distance \(R\) is shown pointing horizontally from the triangle, with the relation:\[ R = \frac{2}{3} h \]The beams are positioned so that they carry equal loads. This requires calculating their positions to balance the water pressure acting on the gate, considering the triangular distribution of force due to water depth.

A water gate is to be reinforced with three horizontal beams (running to the page). If the water acts on one side only to a depth of h=6m, find the positions of the beams measured from the water surface so that each beam will carry an equal load. Gate is fully covered by water. [²] = 24 26 R =

A water gate is to be reinforced with three horizontal beams (running to the page). If the water acts on one side only to a depth of h=6m, find the positions of the beams measured from the water surface so that each beam will carry an equal load. Gate is fully covered by water. [²] = 24 26 R =

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

A water gate is to be reinforced with three horizontal beams (running to the page). If the water acts on one side only to a depth of \(h = 6m\), find the positions of the beams measured from the water surface so that each beam will carry an equal load. Gate is fully covered by water.

**Diagram Explanation:**

The diagram shows a triangular shape representing the water gate. The height \(h\) is marked on the left-hand side, indicating the total depth of the water, which is given as 6 meters. Three horizontal beams are depicted along the vertical side of the triangle, each with distances \(d_1\), \(d_2\), and \(d_3\) from the water surface downwards.

The centroid distance \(R\) is shown pointing horizontally from the triangle, with the relation:

\[ R = \frac{2}{3} h \]

The beams are positioned so that they carry equal loads. This requires calculating their positions to balance the water pressure acting on the gate, considering the triangular distribution of force due to water depth.

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Step 2: Calculation of resultant force acting on the gate and each beam

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Step 3: Calculation of d1

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Step 4: Calculation of d1

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Step 5: Calculation of d2 and d3

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