Question

Во сколько раз высота h подъёма воды в стеблях риса со средним диаметром капилляров d1 = 0,02 мм больше, чем в почве с капиллярами диаметром d2 = 0,3 мм?

Answer 1

Ответ:

Объяснение:

Дано:

d₁ = 0,02 мм

d₂ = 0,30 мм

________________

h₁ / h₂ - ?

Высота поднятия жидкости в капилляре:

h = 2·σ / (ρ·g·r)

Учтем, что радиус в 2 раза меньше диаметра:

r = d /2,

тогда:

h₁ = 4·σ / (ρ·g·d₁)

h₂ = 4·σ / (ρ·g·d₂)

Находим:

h₁ / h₂ = d₂ / d₁

h₁ / h₂ = 0,30 / 0,02 = 30 / 2 = 15

В 15 раз высота поднятия воды в стеблях риса больше высоты поднятия в почве.

Answer 2

Calculating the Ratio of Water Rise in Rice Stems and Soil

To calculate the ratio of the water rise in rice stems to that in soil with capillaries of different diameters, we can use the Hagen-Poiseuille equation, which describes the flow of a fluid through a cylindrical pipe. The equation is given by:

H = (r^4)/(8ηL) * (ΔP)

Where: - H is the height of the water rise - r is the radius of the capillary - η is the viscosity of the fluid - L is the length of the capillary - ΔP is the pressure difference across the capillary

Applying the Hagen-Poiseuille Equation

We can use the Hagen-Poiseuille equation to calculate the ratio of the water rise in the rice stems to that in the soil. Let's denote the ratio as R.

Given: - Diameter of capillary in rice stem, d1 = 0.02 mm - Diameter of capillary in soil, d2 = 0.3 mm

We can calculate the ratio R as follows:

R = (H_rice) / (H_soil) = (r1^4) / (r2^4)

Where: - H_rice is the height of water rise in the rice stem - H_soil is the height of water rise in the soil - r1 is the radius of the capillary in the rice stem - r2 is the radius of the capillary in the soil

Calculating the Ratio

Let's calculate the ratio R using the given diameters of the capillaries.

r1 = d1 / 2 = 0.02 mm / 2 = 0.01 mm

r2 = d2 / 2 = 0.3 mm / 2 = 0.15 mm

Now, we can calculate the ratio R:

R = (0.01^4) / (0.15^4)

Conclusion

By applying the Hagen-Poiseuille equation and calculating the ratio R, we can determine the relationship between the water rise in rice stems and soil with capillaries of different diameters.