Question

Пожалуйста помогите с решением по гидравлике. Воздуховод круглого сечения состоит из двух участков разного диаметра. Скорость газа на первом участке 0,5м/сек, скорость на втором участке 2 м/сек. Диаметр первого участка 60 мм. Найти диаметр второго участка.

Answer 1

Ответ:

24см

Объяснение:

2:0,5=4

4×60=240мм=24см

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Answer 2

Solution for the Diameter of the Second Section in a Round Air Duct

To find the diameter of the second section of the round air duct, we can use the principle of continuity equation in fluid mechanics. According to the continuity equation, the product of the cross-sectional area and the velocity of a fluid remains constant along a streamline.

Let's denote the diameter of the first section as D1 and the diameter of the second section as D2. We are given the velocity of the gas in the first section (V1 = 0.5 m/s) and the velocity of the gas in the second section (V2 = 2 m/s). We need to find D2.

The cross-sectional area of a circular duct can be calculated using the formula:

A = π * (D/2)^2

According to the continuity equation, the product of the cross-sectional area and the velocity remains constant:

A1 * V1 = A2 * V2

Substituting the formulas for the cross-sectional areas:

π * (D1/2)^2 * V1 = π * (D2/2)^2 * V2

Simplifying the equation:

(D1/2)^2 * V1 = (D2/2)^2 * V2

Taking the square root of both sides:

D1/2 * √V1 = D2/2 * √V2

Multiplying both sides by 2:

D1 * √V1 = D2 * √V2

Squaring both sides:

D1^2 * V1 = D2^2 * V2

Now we can substitute the given values and solve for D2:

D1 = 60 mm = 0.06 m V1 = 0.5 m/s V2 = 2 m/s

0.06^2 * 0.5 = D2^2 * 2

Simplifying the equation:

0.0018 = 2D2^2

Dividing both sides by 2:

0.0009 = D2^2

Taking the square root of both sides:

D2 = √0.0009

Calculating the value of D2:

D2 ≈ 0.03 m

Therefore, the diameter of the second section of the round air duct is approximately 0.03 meters.

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