# Why are my empirical and theoretical value of mass flow rate in solid propellant rockets not similar?

For a rocket of:

• fuel mass $$m_f$$ = 6 kg,
• Thrust = 3.1 kN, (vs 4k using reducing catalyst to delay burn time)
• total powered burn time, $$t_b$$ = 3.5 s, (using reducing catalyst vs 1.8 sec)

This gives me the burn rate mass flow rate, 6/3.5 = 1.71 kg/s. But theoretically, it should be around 4.8 kg/s. Using

$$\dot{m} = \rho_p A_b r$$ where

• $$\rho_p$$ = Density of propellant
• $$A_b$$ = Burning surface area of the cylinder propellant (circular bore grain shape)
• $$r$$ = rate of propellant burn

The rate is caluculated using: $$r = a P_c^n$$ where $$a$$, $$n$$ are empirical coefficients and $$P_c$$ is the chamber pressure

So, if reverse the steps to find pressure, I get 25 psi or 0.177 MPa.

But, theoretically this should be 4.8 kg/s for my propellant KNSU with $$A_b = 0.19 m^2$$ ($$h=0.8m$$, $$r_{in} = 0.076m$$, using $$A_b = \pi r_{in} h$$) and for chamber press of 4.8 MPa or 700 psi with $$\rho_p$$=1.889 g/$$cm^3$$ a=8.26 and n=0.319 using the two relation above. Could anyone share what could cause such discrepancy?

• Where are you getting that 0.19m2 burn area? If its a flat circle(end burning), that's a circle 50 centimetres wide. If it is a hollow-core cylinder of inner diameter 10mm, as per your previous questions, it is a rocket motor SIX METRES in length. Fix your burn area, and maybe your calculations will make more sense. Sep 26, 2021 at 12:48
• Hello @PcMan , Thank you. The combustion chamber is 80 cm long and 0.0762 cm inner radius. Sep 26, 2021 at 14:14
• The values of $a$, $\rho_p$, and $n$ would be useful information to include in the question Sep 26, 2021 at 15:13
• Argh! units are important, and accuracy is important. If your inner radius of your engine is 0.0762cm, then it is smaller than a toothpick! I'm pretty sure this is an error in the number, not in the design? Also, i see your question states this as r=0.076m. which sounds suspiciously large. That's the size of a large cereal bowl. Sep 26, 2021 at 15:59
• Thank you @PcMan, you are right. I was using the the diameter instead of the radius which is 0.0762/2 m = 0.0381m. The theoretical mass flow rate and burn rate are now 2.4 kg/s (29% higher) and 10 mm/s. As compared to test values of q=1.71 kg/s and r = 4.76 mm/s. Can I attribute this difference to the addition of -ve catalyst in the propellant? Sep 27, 2021 at 3:38