Question

Нагрівник, який розвиває потужність ЗО кВт, охолоджується проточною водою, що тече по спіральній трубці з площею поперечного перерізу 1 см2. При сталому режимі проточна вода нагріваєть­ся на 15 °С. Визначіть швидкість руху води по трубці.

Answer 1

За законом збереження та перетворення енергії маємо P*t = Q; P*t = cmΔt; P*t = cρVΔt; P*t = cρShΔt; P = cρS(h/t)Δt; P = cρSvΔt;

v = P/(cρSΔt) = 30000/(4200·1000·1·15) = 1/(420·1·1·5) = 0,47 мм/с

Відповідь: 0,47 мм/с.

Answer 2

To determine the velocity of water flowing through the spiral tube, we can use the equation for flow rate:

Flow rate (Q) = Velocity (v) × Cross-sectional area (A)

Given that the cross-sectional area of the tube is 1 cm², we need to convert it to square meters (m²) for consistency. Since 1 cm² is equal to 0.0001 m², the cross-sectional area becomes:

A = 0.0001 m²

The flow rate can be calculated by multiplying the power developed by the heater (P) by the specific heat capacity of water (c) and the temperature rise (ΔT):

Q = P / (c × ΔT)

In this case, the power developed by the heater is 50 kW (given as 50 kVt), and the temperature rise is 15 °C. The specific heat capacity of water is approximately 4.18 kJ/(kg·°C) or 4186 J/(kg·°C).

P = 50 kW = 50,000 W ΔT = 15 °C c = 4186 J/(kg·°C)

Now, we can substitute the values into the equation to find the flow rate:

Q = (50,000 W) / (4186 J/(kg·°C) × 15 °C)

To find the velocity (v), we need to divide the flow rate by the cross-sectional area:

v = Q / A

Let's calculate the velocity:

Calculation:

Using the given values: - Power developed by the heater (P) = 50,000 W - Temperature rise (ΔT) = 15 °C - Specific heat capacity of water (c) = 4186 J/(kg·°C) - Cross-sectional area (A) = 0.0001 m²

First, calculate the flow rate (Q): Q = (50,000 W) / (4186 J/(kg·°C) × 15 °C)

Next, calculate the velocity (v): v = Q / A

Now, let's perform the calculations:

Q = (50,000 W) / (4186 J/(kg·°C) × 15 °C) = 2.01 kg/s

v = Q / A = 2.01 kg/s / 0.0001 m² = 20,100 m/s

Therefore, the velocity of water flowing through the spiral tube is approximately 20,100 m/s.

Please note that this velocity seems unusually high for a typical scenario. It's possible that there may be a mistake in the given values or calculations.