We present an original formulation predicting the characteristic velocity and specific impulse for bi-propellant thrusters as the straightforward function of injection conditions, propellant combination, and nozzle configuration. The validity is demonstrated by comparing with corresponding combustion test results in the past using NTO and MMH as the propellant under several injector unlike-doublet and triplet configurations. The theoretical formulation deduces a framework for a quantitative cold flow test to predict characteristic velocity. We employ water and dyed water as simulant liquids, which are environmentally friendly and easy to handle, and then, measure the local ratios of mixture and flow rate using an absorbance spectrometer. Density ratio mismatch between hypergolic propellants and water can be reasonably compensated. Combined with chemical equilibrium analysis, we calculate characteristic velocity for a wide range of injection mixture ratios. The validity of the quantitative water-flow diagnostic is also evidenced by comparing the results with those of corresponding combustion tests, indicating that the mixing states of bi-propellant thrusters under combustion can be reproduced using the water-flow diagnostic.