To calculate the rate of heat loss from the steam pipe, we can use the heat transfer equation for a cylindrical surface. The formula for heat transfer through a cylindrical pipe is:

$Q = h \cdot A \cdot (T_{pipe} - T_{ambient})$

Where:

• $Q$ is the rate of heat loss (W),
• $h$ is the combined heat transfer coefficient (W/m²·K),
• $A$ is the surface area of the pipe (m²),
• $T_{pipe}$ is the temperature of the pipe surface (°C),
• $T_{ambient}$ is the ambient temperature (°C).

Given values:

• Pipe outer diameter $D = 10 \, \text{cm} = 0.1 \, \text{m}$,
• Pipe length $L = 50 \, \text{m}$,
• $h = 20 \, \text{W/m²·K}$,
• $T_{pipe} = 150 \, \text{°C}$,
• $T_{ambient} = 19 \, \text{°C}$.

Surface Area Calculation:

The surface area $A$ of the cylindrical pipe is calculated by the formula:

$A = \pi \cdot D \cdot L$

Now, we can substitute all the values and calculate the rate of heat loss.

Let me calculate that for you. math

Given values

D = 0.1 # Diameter of the pipe in meters L = 50 # Length of the pipe in meters h = 20 # Heat transfer coefficient in W/m²·K T_pipe = 150 # Temperature of the pipe in °C T_ambient = 19 # Ambient temperature in °C

Calculate the surface area of the pipe

A = math.pi * D * L

Calculate the rate of heat loss

Q = h * A * (T_pipe - T_ambient) QThe rate of heat loss from the steam pipe is approximately 41,155 watts (W).

Would you like more details or clarification on the steps?

Here are some related questions for further exploration:

1. How does the heat transfer coefficient affect the rate of heat loss in this scenario?
2. What are the effects of changing the length of the pipe on heat loss?
3. How would the heat loss change if the ambient temperature were higher?
4. What would happen if the pipe's insulation were increased in thickness or efficiency?
5. How does the diameter of the pipe influence heat transfer in this case?

Tip: Increasing the heat transfer coefficient or the surface area of the pipe can significantly raise the rate of heat loss.