# Cooling jacket calculation issue [duplicate]

I'm going through How to Design, Build, and Test Small Liquid-Fuel Rocket Engines. The reference explains how to calculate the water flow gap for the cooling jacket that surrounds the combustion chamber with this equation:

A = $$(\frac{\Pi}{4}) (D_2^2 - D_1^2)$$

where $$D_2$$ is the diameter of the outer wall of the cooling jacket and $$D_1$$ is the diameter of the inner wall of the cooling jacket (where $$D_1$$ = $$D_c$$ + 2$$t_w$$, the diameter of the chamber wall = 1.2 in and the thickness of the chamber wall = .09375 in).

Using the annular flow velocity equation with the given figures (sorry for imperial): flow velocity of water $$v_w$$ = 30 $$\frac{ft}{s}$$, flow rate based on a desired temperature rise of the water $$w_w$$ = .775 $$\frac{lb}{s}$$, and water density $$\rho$$ = 62.4 $$\frac{lb}{ft^3}$$, I am to solve for $$D_2$$ using this equation:

A = $$\frac{w_w}{\rho v_w}$$

solving for $$D_2$$:

$$D_2$$ = $$\sqrt{\frac{4w_w}{v_w \rho \pi} + (D_c + 2t_w)^2}$$ (remembering to convert $$D_c$$ and $$t_w$$ to feet from inches)

The issue i'm having is when I calculate their expected $$D_2$$ figure I get 1.415 in., but in their calculation they get 1.475 in. which may not sound like much, but when calculating the actual flow gap of the cooling jacket using $$\frac{D_2-D_1}{2}$$, with their 1.475 in. diameter the flow gap is .0425 in. But with the correct $$D_2$$ figure of 1.415 in., the flow gap should be $$\frac{1.415-(1.2-2*.09375)}{2}$$ = .01375 in.

Their answer is 3 times greater than what it should be, so my question is when doing my own calculations for my rockets dimensions/figures, should I still use the above equations to figure out the flow gap? And which figure is correct, a $$D_2$$ of 1.415 in. or 1.475 in.?

• Already asked here:space.stackexchange.com/questions/26076/… but the site does not allow closing as duplicate. Commented Mar 15, 2019 at 17:31
• It was asked there but unfortunately there was no insight given as to whether or not it would be ok to continue the design of a rocket with those figures. I was hoping that by asking anyone with experience designing something like this could lend me advice on how to continue, because the difference in flow gap seems pretty significant.
– MAP3
Commented Mar 15, 2019 at 17:37
• see my answer to the old question. I found a version of the text with an addendum that references this. Commented Mar 16, 2019 at 16:45
• Thank you for sharing this, in the additions and corrections page it is mentioned that "The calculation in the Propellant Choice section assumes that there are no losses; i.e., that the "maximum theoretical" Isp will be that which is achieved. There are numerous loss terms not accounted for; hence the flowrate given is incorrect." Would continuing with the design and eventual testing of a rocket using the flowrate derived from the original text be much of an issue? Is the result just going to be less thrust produced by the rocket or something more serious?
– MAP3
Commented Mar 19, 2019 at 15:24
• reduced Isp is a loss of efficiency - it means either the same thrust with more propellant usage or less thrust for the same propellant usage. Without detailed knowledge of the system I couldn't say which. Commented Mar 19, 2019 at 17:16