Our rocket team is trying to finalize the design of our injector for a small liquid rocket engine. The current analysis challenge is verifying the correct pressure drop across the annular orifice leading to the combustion chamber which the Kerosene flows through.
The current equation we are working with is this one provided in Mathwork's documentation.
Because we know the inner diameter of the annulus (the pintle body OD), and the properties of the liquid flowing through the reservoir leading to the injector orifice, we were able to calculate an orifice OD of 1.11inches.
The reason we are suspicious of this equation is because it makes reference to laminar flow, where we have a pretty high mass flow, and hence high flow velocity.
Are there any simple (undergraduate level) resources that can further inform us how to either directly calculate diameter, or could let us converge on a discharge coefficient and diameter through numerical methods?
Thanks! Here is a quick picture of our injector if that helps. https://i.imgur.com/BUb8DG3.png