Question

The base of a greenhouse is a circle with radius 3 metres. There is a central irrigation sprinkler in the roof, which waters the greenhouse unevenly. The rate of irrigation r metres from the centre of the greenhouse (measured along the ground) is r+2/r+1​ litres of water per square metre per day. Figure 5: Irrigation rate across greenhouse: light colours are higher, dark are lower (a) Let r0​ and Δr₀ be positive constants, with 0≤r0₀≤r0₀+Δr₀​≤3. Interpret, in terms of our model, 2πr₀Δr₀⋅r₀+2​/r₀+1when Δr₀​ is small. (Remember to include units, as always.) (b) Interpret, in terms of our model, the value you computed in 3 (b). (c) Interpret, in terms of our model, the value you computed in 3(e).

Answer 1

To calculate the amount of sunlight concentrated onto the pipe, multiply the insolation by the area of the pipe. To calculate the temperature increase of the fluid per meter of pipe, use the formula Q = mcΔT.

Step-by-step explanation:

b. Amount of sunlight concentrated onto the pipe:

To calculate the amount of sunlight concentrated onto the pipe per meter, we can multiply the insolation (incident solar radiation) by the area of the pipe.

The area of the pipe is the circumference multiplied by the length of the pipe.

So, the amount of sunlight concentrated onto the pipe per meter is 0.900 kW/m² * (2π * r * h), where r is the radius of the pipe and h is the height or length of the pipe.

c. Temperature increase of the fluid per meter of pipe:

To calculate the temperature increase of the fluid per meter of pipe over a period of one minute, we can use the formula Q = mcΔT, where Q is the heat transferred, m is the mass of the fluid, c is the specific heat capacity of the fluid, and ΔT is the change in temperature.

In this case, the heat transferred is equal to the amount of sunlight concentrated onto the pipe per meter (calculated in part b), and the mass of the fluid can be calculated using its volume and density.

By solving for ΔT, we can find the temperature increase of the fluid per meter of pipe over one minute.