Question

Prove that, triangular hydraulic section is half of rectangular. (please help me, it's an emergency )

Answer 1

Step-by-step explanation:

proof that the flow area of a triangular hydraulic section is half of a rectangular section with the same base and height.

Let's consider a rectangular channel with width "b" and height "h". The flow area of the rectangular channel can be calculated as:

A_rectangular = b * h

Now, let's consider a triangular channel with base "b" and height "h". The flow area of the triangular channel can be calculated as:

A_triangular = 0.5 * b * h

To prove that the flow area of the triangular channel is half of the rectangular channel, we can take the ratio of the two flow areas:

A_triangular / A_rectangular = (0.5 * b * h) / (b * h)

Simplifying this expression, we get:

A_triangular / A_rectangular = 0.5

Therefore, we can conclude that in the case of a rectangular channel with width "b" and height "h", the flow area of a triangular channel with base "b" and height "h" is half of the flow area of the rectangular channel.

However, it's important to note that this result only holds true for this specific case where the rectangular channel and the triangular channel share the same base and height. If the dimensions of the channels differ, the flow area of the triangular channel will not necessarily be half of the flow area of the rectangular channel.

NOTE. (just a concern)

it's important to note that this is only true for a specific case, and it's not a general rule that applies to all triangular and rectangular sections. In general, the flow area of a hydraulic section depends on its geometry and cannot be determined solely based on the shape of the section.

Answer 2

To prove that the triangular hydraulic section is half of the rectangular section, we need to compare the areas of both shapes.

Let's consider a rectangular hydraulic section with width "b" and height "h". The area of the rectangular section is given by:

A_rectangular = b * h

Now, let's consider a triangular hydraulic section with width "b" and height "h". The area of the triangular section is given by:

A_triangular = 1/2 * b * h

We can see that the area of the triangular hydraulic section is half of the area of the rectangular section:

A_triangular = 1/2 * A_rectangular

This can be easily verified by dividing the rectangular section into two equal triangles along the diagonal, as shown in the diagram below:


+----------------------+
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+----------+-----------+
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+-----------+

The two resulting triangles have the same width "b" and height "h/2". The area of each triangle is:

A_triangle = 1/2 * b * h/2 = 1/4 * b * h

The total area of the two triangles is:

A_triangular = 2 * A_triangle = 2 * 1/4 * b * h = 1/2 * b * h

Therefore, we have shown that the triangular hydraulic section is half of the rectangular section.