Question

Колесо турбины ГЭС совершает 90 оборотов в минуту. Определить центростремительное ускорение концов лопастей турбины, линейная скорость которых 40 м/с. Каков диаметр колеса турбины?

Answer 1

Ответ:

Д=8,4 м, а ц=170 м/с

Объяснение:

Answer 2

Ответ:  376,5м/с²; 8,5м

Объяснение:

Дано:

n=90 об/мин

V=40м/с

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ац-?; d-?

Угловая скорость турбины равна:

ω=πn/30=3,14*90/30=9,42рад/с

Линейную скорость концов лопастей находим по формуле:

V=ωR

Отсюда:

R=V/ω=40/9,42=4,25м

Диаметр колеса турбины равен 2R

d=2*4,25=8,5м

Центростремительное ускорение равно:

ац=V²/R=40²/4,25=376,5м/с²

Answer 3

Calculation of Centripetal Acceleration and Diameter of Turbine Wheel

To determine the centripetal acceleration and diameter of the turbine wheel, we can use the following formulas:

1. Centripetal acceleration (a): - The centripetal acceleration is given by the formula: a = (v^2) / r - Where v is the linear velocity of the turbine blade tips and r is the radius of the turbine wheel.

2. Linear velocity (v): - The linear velocity is given by the formula: v = ω * r - Where ω is the angular velocity of the turbine wheel and r is the radius of the turbine wheel.

3. Angular velocity (ω): - The angular velocity is given by the formula: ω = (2π * n) / 60 - Where n is the number of revolutions per minute (RPM) of the turbine wheel.

Let's calculate the centripetal acceleration and diameter of the turbine wheel using the given information:

Given: - The turbine wheel makes 90 revolutions per minute (RPM). - The linear velocity of the turbine blade tips is 40 m/s.

Calculation:

1. Angular velocity (ω): - Using the formula ω = (2π * n) / 60, where n = 90 RPM: - ω = (2π * 90) / 60 = 3π rad/s.

2. Linear velocity (v): - Using the formula v = ω * r, where v = 40 m/s: - 40 = 3π * r - r = 40 / (3π) ≈ 4.24 m.

3. Centripetal acceleration (a): - Using the formula a = (v^2) / r, where v = 40 m/s and r = 4.24 m: - a = (40^2) / 4.24 ≈ 376.42 m/s^2.

Therefore, the centripetal acceleration of the turbine blade tips is approximately 376.42 m/s^2 and the diameter of the turbine wheel is approximately 8.48 m (twice the radius).

Please note that the search results provided by You.com did not contain relevant information for this specific calculation. The calculation was performed using the given formulas and the provided values.