Question

В горизонтальной трубе газопровода диаметром 40 см течет газ со скоросью 100 см/2.Труба расширяется и газ стал двигаться со скоростью 0 5 м/с.Каким стал диаметр трубы

Answer 1

Объяснение:

Ответ: диаметр2 = 28 см.

Answer 2

Calculation of the new diameter of the pipe

To determine the new diameter of the pipe, we can use the principle of conservation of mass. According to this principle, the mass flow rate of the gas remains constant throughout the pipe, assuming no leaks or additional sources/sinks of gas.

The mass flow rate of the gas can be calculated using the formula:

Mass flow rate = density × velocity × cross-sectional area

Since the density of the gas remains constant, we can write:

Mass flow rate1 = Mass flow rate2

The cross-sectional area of a pipe is given by the formula:

Area = π × (diameter/2)^2

Let's denote the initial diameter of the pipe as D1 and the final diameter as D2. We are given the initial velocity of the gas (V1 = 100 cm/s) and the final velocity of the gas (V2 = 0.5 m/s).

Using the equation for the mass flow rate and the cross-sectional area, we can set up the following equation:

Density × V1 × (π × (D1/2)^2) = Density × V2 × (π × (D2/2)^2)

Simplifying the equation, we can cancel out the density and π:

V1 × (D1/2)^2 = V2 × (D2/2)^2

Now, let's substitute the given values into the equation and solve for D2:

100 cm/s × (40 cm/2)^2 = 0.5 m/s × (D2/2)^2

Simplifying further:

100 cm/s × 20 cm^2 = 0.5 m/s × (D2/2)^2

2000 cm^3/s = 0.5 m/s × (D2/2)^2

Converting cm^3/s to m^3/s:

2000 cm^3/s = 0.002 m^3/s

Substituting this value into the equation:

0.002 m^3/s = 0.5 m/s × (D2/2)^2

Simplifying:

(D2/2)^2 = 0.002 m^3/s / 0.5 m/s

(D2/2)^2 = 0.004 m^2

Taking the square root of both sides:

D2/2 = sqrt(0.004 m^2)

D2/2 = 0.063 m

Multiplying both sides by 2:

D2 = 0.126 m

Therefore, the new diameter of the pipe is 0.126 meters.

Please note that the calculations assume ideal conditions and do not take into account factors such as friction or changes in gas properties.