SDP3x: Add model for pitot pressure drop

Tools/models/sdp3x_pitot_model.py

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+"""
+Copyright (c) 2017, Sensirion AG
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+* Redistributions of source code must retain the above copyright notice, this
+  list of conditions and the following disclaimer.
+
+* Redistributions in binary form must reproduce the above copyright notice,
+  this list of conditions and the following disclaimer in the documentation
+  and/or other materials provided with the distribution.
+
+* Neither the name of Sensirion AG nor the names of its
+  contributors may be used to endorse or promote products derived from
+  this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+"""
+
+
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+
+## differential pressure, sensor values in Pascal
+dp_SDP33=np.linspace(0,800,100)
+
+
+
+## total length tube in mm = length dynamic port+ length static port; compensation only valid for inner diameter of 1.5mm
+l_tube=400
+
+## densitiy air in kg/m3
+rho_air=1.29
+
+
+## flow through sensor
+flow_SDP33=(300.805 - 300.878/(0.00344205*dp_SDP33**0.68698 + 1))*1.29/rho_air
+
+## additional dp through pitot tube
+dp_Pitot=28557670. - 28557670./(1 + (flow_SDP33/5027611)**1.227924)
+
+
+## pressure drop through tube
+dp_Tube=flow_SDP33*0.000746124*l_tube*rho_air
+
+## speed at pitot-tube tip due to flow through sensor
+dv=0.0331582*flow_SDP33
+
+## sum of all pressure drops
+dp_tot=dp_SDP33+dp_Tube+dp_Pitot
+
+## computed airspeed without correction for inflow-speed at tip of pitot-tube
+airspeed_uncorrected=np.sqrt(2*dp_tot/rho_air)
+
+## corrected airspeed
+airspeed_corrected=airspeed_uncorrected+dv
+
+
+## just to compare to value without compensation
+airspeed_raw=np.sqrt(2*dp_SDP33/rho_air)
+
+
+
+
+plt.figure()
+plt.plot(dp_SDP33,airspeed_corrected/airspeed_raw)
+plt.xlabel('differential pressure raw value [Pa]')
+plt.ylabel('correction factor [-]')
+plt.show()
+
+
+
+plt.figure()
+plt.plot(airspeed_corrected,(airspeed_corrected-airspeed_raw)/airspeed_corrected)
+plt.xlabel('airspeed [m/s]')
+plt.ylabel('relative error [-]')
+plt.show()