Pump-rate as a function of supply voltage.

The pump-rate calibration was done by pumping against a fixed pressure of 1200 dbars. This was accomplished using a pressure relief valve to vent water as necessary in order to keep the pressure from rising above 1200 dbars. By measuring the time required to pump a fixed volume (ie., 4 A/D counts) then the pump-rate at a given voltage is known. A lab power supply was used to supply current at a voltage that was fixed while each pump-rate measurement was made.

 

Table: This table shows the relation between pump-rate and supply voltage at a pressure of 1200 dbar. The right-most two columns show the voltage, $\tilde{V}$, predicted by the model (see equation (3)) and the voltage error, $\delta V = V-\tilde{V}$.

V	i	$\frac{dv}{dt}$	$\tilde{V}$	$\delta V$
Volts	Amps	ml$\cdot$s-1	Volts	Volts
15.00	0.510	0.165	14.45	0.55
14.00	0.515	0.165	14.48	-0.48
13.00	0.520	0.140	12.68	0.32
12.00	0.520	0.133	12.19	-0.19
11.00	0.515	0.122	11.31	-0.31
10.00	0.525	0.104	10.03	-0.03
9.00	0.520	0.090	9.02	-0.02
8.00	0.530	0.074	7.84	0.16

 

Least-squares methods were used to fit the model of the pump motor (see equation (3)) to the data from Table 3. The optimal parameter values $R=\ensuremath{4.6\Omega}$ and $K=\ensuremath{73.7\frac{\textrm{V}\cdot\textrm{s}}{\textrm{ml}}}$ yielded an RMS misfit of only 0.31 V. The right-most two columns of Table 3 show the predicted voltage, $\tilde{V}$, and voltage error, $\delta V = V-\tilde{V}$. The pump-rate is a known and well-behaved function of pressure (ie., current) and supply voltage.