From the HBD Archive
From: piatz@fig.cray.com (Steve Piatz)
Subject: Adjusting specific gravity
Date: 1992-07-08 17:24:08 GMT

I recently had a need to determine the change in specific gravity due
to dilution with addition water. I ended up boiling my imperial stout
down to 4.75 gallons while getting my 60 minute boil after adding the
hops. I decided not to dilute until I went to the secondary and needed
to adjust my specific gravity measured in the primary. TNCJOHB, page
381 gives some tables for adjusting the specific gravity.
Unfortunately, they didn't come close to the 1.110 gravity I had. So I
decided to figure out the corrections using the following (I hope my
memory of physics classes from long ago is correct):

OG = the original gravity
FG = the final gravity
dvp = the additional water as a percent (5% == 0.05)

FG = (OG + dvp) / (1.0 + dvp)

Using the above, the following program will produce a simple
adjustment table
==================== cut here ===================
#include <stdio.h>
#define NUM_PERCENT 10 /* number of columns */
#define NUM_GRAVITY 30 /* number of rows */
#define PERCENT_STEP 0.05 /* percentage per column */
#define GRAVITY_STEP 0.005 /* gravity per row */
#define INITIAL_GRAVITY 1.010 /* gravity for first row */
#define INITIAL_PERCENT PERCENT_STEP /* percentage for first column */
main ()
{
int i;
int j;
float og, fg;
float dv;
float dvp;
printf (" | Dilution By\n");
printf (" O.G. | ");
for (j = 0; j < NUM_PERCENT; j++)
printf (" %3.0f%% ", 100.0 * PERCENT_STEP * (1 + j));
printf ("\n");
printf ("-------|-");
for (j = 0; j < NUM_PERCENT; j++) printf ("-------");
printf ("\n");
og = INITIAL_GRAVITY - GRAVITY_STEP;
for (i = 0; i < NUM_GRAVITY; i++) {
og += GRAVITY_STEP;
printf ("%6.3f | ", og);
dvp = INITIAL_PERCENT - PERCENT_STEP;
for (j = 0; j < NUM_PERCENT; j++) {
dvp += PERCENT_STEP;
fg = (og + dvp) / (1.0 + dvp);
printf ("%6.3f ", fg);
}
printf ("\n");

}
exit ();
}

====================== cut here ======================

The resulting table is

| Dilution By
O.G. | 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%
- -------|-----------------------------------------------------------------------
1.010 | 1.010 1.009 1.009 1.008 1.008 1.008 1.007 1.007 1.007 1.007
1.015 | 1.014 1.014 1.013 1.012 1.012 1.012 1.011 1.011 1.010 1.010
1.020 | 1.019 1.018 1.017 1.017 1.016 1.015 1.015 1.014 1.014 1.013
1.025 | 1.024 1.023 1.022 1.021 1.020 1.019 1.019 1.018 1.017 1.017
1.030 | 1.029 1.027 1.026 1.025 1.024 1.023 1.022 1.021 1.021 1.020
1.035 | 1.033 1.032 1.030 1.029 1.028 1.027 1.026 1.025 1.024 1.023
1.040 | 1.038 1.036 1.035 1.033 1.032 1.031 1.030 1.029 1.028 1.027
1.045 | 1.043 1.041 1.039 1.037 1.036 1.035 1.033 1.032 1.031 1.030
1.050 | 1.048 1.045 1.043 1.042 1.040 1.038 1.037 1.036 1.034 1.033
1.055 | 1.052 1.050 1.048 1.046 1.044 1.042 1.041 1.039 1.038 1.037
1.060 | 1.057 1.055 1.052 1.050 1.048 1.046 1.044 1.043 1.041 1.040
1.065 | 1.062 1.059 1.057 1.054 1.052 1.050 1.048 1.046 1.045 1.043
1.070 | 1.067 1.064 1.061 1.058 1.056 1.054 1.052 1.050 1.048 1.047
1.075 | 1.071 1.068 1.065 1.062 1.060 1.058 1.056 1.054 1.052 1.050
1.080 | 1.076 1.073 1.070 1.067 1.064 1.062 1.059 1.057 1.055 1.053
1.085 | 1.081 1.077 1.074 1.071 1.068 1.065 1.063 1.061 1.059 1.057
1.090 | 1.086 1.082 1.078 1.075 1.072 1.069 1.067 1.064 1.062 1.060
1.095 | 1.090 1.086 1.083 1.079 1.076 1.073 1.070 1.068 1.066 1.063
1.100 | 1.095 1.091 1.087 1.083 1.080 1.077 1.074 1.071 1.069 1.067
1.105 | 1.100 1.095 1.091 1.087 1.084 1.081 1.078 1.075 1.072 1.070
1.110 | 1.105 1.100 1.096 1.092 1.088 1.085 1.081 1.079 1.076 1.073
1.115 | 1.110 1.105 1.100 1.096 1.092 1.088 1.085 1.082 1.079 1.077
1.120 | 1.114 1.109 1.104 1.100 1.096 1.092 1.089 1.086 1.083 1.080
1.125 | 1.119 1.114 1.109 1.104 1.100 1.096 1.093 1.089 1.086 1.083
1.130 | 1.124 1.118 1.113 1.108 1.104 1.100 1.096 1.093 1.090 1.087
1.135 | 1.129 1.123 1.117 1.112 1.108 1.104 1.100 1.096 1.093 1.090
1.140 | 1.133 1.127 1.122 1.117 1.112 1.108 1.104 1.100 1.097 1.093
1.145 | 1.138 1.132 1.126 1.121 1.116 1.112 1.107 1.104 1.100 1.097
1.150 | 1.143 1.136 1.130 1.125 1.120 1.115 1.111 1.107 1.103 1.100
1.155 | 1.148 1.141 1.135 1.129 1.124 1.119 1.115 1.111 1.107 1.103


Steve Piatz piatz@cray.com

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