Help with a problem to design a vessel

[theone!]

The problem involves a a heater and three jacketed reactors. The reactors are heated by water supplied by the heater.

Determine the heater size(in kW) required for this service if the heater is to be
sized so that it is large enough to handle all three reactors when they operate at full load

do I just treat the jacketed vessels like heat exchangers;

$\dot Q=U A_s \Delta T$ with $\frac{1}{U A_s}=\frac{1}{h_i A_i} + \frac{ln(D_o/D_i)}{2 \pi k L} + \frac{1}{h_o A_o}$

and then multiply $\dot Q$ by 3 to get the heater size?

Determine the appropriate pipe sizes for the main water supply and return lines.
the system. There should be two different pipe sizes: one for the main supply/return line and another for the lines connecting the reactors to the main supply lines.

is this just an application of

$\frac{p_1}{y} + \frac{V_1}{2g} + z_1 = \frac{p_2}{γ} + \frac{V_2}{2g} + z_2 + \frac{V_2}{2g} [ \frac{fL}{D} + K ]$

and I should solve for the diameter?

 

[CWatters]

The device I'm using to type this on doesn't allow me to see your equations correctly so I haven't been able to check those but..

The problem statement appears to gives you enough info to work out the power consumed by each reactor... You have the flow rate and the temperature drop and can look up the specific heat capacity of water. Multiply by three and you have the power that the heater would need to deliver.

I can't help with the pipe sizing sorry.

 

[theone!]

The device I'm using to type this on doesn't allow me to see your equations correctly so I haven't been able to check those but..

The problem statement appears to gives you enough info to work out the power consumed by each reactor... You have the flow rate and the temperature drop and can look up the specific heat capacity of water. Multiply by three and you have the power that the heater would need to deliver.

I can't help with the pipe sizing sorry.

thanks!

about the pipe diameters, I think I have the equation to get them but it looks like I need the flow rate of the water. (The only flow rate info I'm given is the max allowable flow rate of 50 USGPM through the jacket)

Another question of the project asks me to "determine the required pump head and flow rate for your design"

So I was wondering if I should pick some pump, plot the system curve and pump curve, get the operating pump head and flow rate at the intersection, and then use that flow rate to get the diameters?

 

[CWatters]

I never studied this but...

The problem statement describes the pipework. It looks like there is a main supply and return which will carry 3 x 50usgpm plus branch pipes to each reactor that will carry 1 x 50usgpm each.

Its not my field but I imagine you need to make a drawing and mark it up with the flow rates and calculate the pressure losses in each section. Calculate the pressure loss around the loop including that in the heater (gives you the pump head required). That and the flow rate should allow you to work out the pump power? I think!

 

[Fulbring]

The problem involves a a heater and three jacketed reactors. The reactors are heated by water supplied by the heater.

Determine the heater size(in kW) required for this service if the heater is to be
sized so that it is large enough to handle all three reactors when they operate at full load

do I just treat the jacketed vessels like heat exchangers;

$\dot Q=U A_s \Delta T$ with $\frac{1}{U A_s}=\frac{1}{h_i A_i} + \frac{ln(D_o/D_i)}{2 \pi k L} + \frac{1}{h_o A_o}$

and then multiply $\dot Q$ by 3 to get the heater size?

Determine the appropriate pipe sizes for the main water supply and return lines.
the system. There should be two different pipe sizes: one for the main supply/return line and another for the lines connecting the reactors to the main supply lines.

is this just an application of

$\frac{p_1}{y} + \frac{V_1}{2g} + z_1 = \frac{p_2}{γ} + \frac{V_2}{2g} + z_2 + \frac{V_2}{2g} [ \frac{fL}{D} + K ]$

and I should solve for the diameter?

Hey, so did you end up solving the problem with the P&ID? Is there any chance you can share it?