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Unit 4 P2

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P=P_1 +C_p*(V-V_0 )
[9]
where P and P1 are the measured and atmospheric pressures in psia, Cp is the calibration constant in psia/volts, V is the transducer voltage, and V0 is the offset voltage.

RESULTS AND DISCUSSION To convert the measured voltages to pressures, we first determined the calibration constants of transducers 2 and 3 for each of the trials ranging from 6 to 14 psig. To do this, we calculated the measured shock wave velocity for each trial by dividing the distance between transducers 2 and 3 (0.548 m) by the measured time difference between the peak measured voltages. Next, assuming T = 70° F and γ = 1.4 (for air), we calculated the speed of sound and Mach number using equations 2 and 3. We used this measured Mach number …show more content…

Calibration constants, in units of psia/volt, for transducers 2 and 3 at different driver conditions.

The results show that the calibration constants vary slightly based on the driver pressure due to the different gain settings used. However, the calibration constants change dramatically if the shock tube is closed, or if a different driver gas is used.
Using the calculated calibration constants, we converted the measured voltage data to absolute pressure data. The pressure data for driver pressures of 6, 10, and 14 psig have been plotted versus time in Figures 2-4 below.
Figures 2-4. Pressure transducer data for driver pressures of 6, 10, and 14 psig in an open shock tube.
These plots clearly show an identical trend across all three driver pressures – a discontinuous rise in pressure in wake of the shock wave followed by a continuous drop in pressure below Patm = 14.7 psi in wake of the reflected rarefaction wave before finally re-pressurizing back to atmospheric pressure. In addition, as the driver pressure increased, the magnitude of the peak and trough pressures, P2 and P6, …show more content…

In Figure 8b for transducer 3, which is closer to the right wall, we see a discontinuous increase from P1 to P2 in wake of the shock wave, as expected, but also an additional discontinuous increase from P2 to P5 due to the reflected shock wave. Afterwards, we notice a continuous drop in the pressure from P5 to P1 due to the reflected rarefaction wave. However, in Figure 8a for transducer 2, we see that pressure drop due to the reflected rarefaction wave occurs before the pressure rise due to the reflected shock wave. This results in a strange feature in the graph just to the left of t = 0.01s, in which the pressure begins to drop continuously, but halfway through rises discontinuously before dropping continuously once again. Due to these reflection related phenomena, the pressure traces (for transducers 2 and 3) for closed condition not only look very different from each other, but also different when compared to the open

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