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• The relation between mdot and Cd is as follows: mdot = Cd * A_inj * sqrt(2*rho*dP). If injector dP is not sufficient to choke the flow, we can assume that Cd is constant throughout a cold flow test. We can then integrate both sides of this equation, which allows us to put this equation in terms of more parameters that we know (i.e. the total mass of the water that flowed through the injector). The equation becomes 

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  body m_{discharged}

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  body =

   

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  body C_d

   

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  body *

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  body A_{inj}

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  body *

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  body \sqrt(2*rho)

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  body \int_{t_1}^{t_2} \sqrt(\Delta P) \,dt

  . To get deltaP, we will simply have a pressure transducer port linked to our manifold. We can then take the square root of our recorded pressure data and integrate that throughout the duration of the test. For this test, we will enforce the pressure inside the manifold to be equal to the pressure drop across the injector for hotfire, as the water will feel the ambient pressure once it leaves the injector, not the chamber pressure. This should allow us to get Cd!

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