Sunday, May 4, 2014

Can your liver actually process a drink per hour? How slow do you have to drink to stay sober?

We have all heard the rule of thumb that your liver can process one beer an hour. I've never been sold on the claim, here's why.

While there is no agreement on the exact rate, most research has concluded that the liver can process about 0.25 fluid ounces of alcohol per hour (some find a higher rate, while some lower). This rate is largely independent of your weight or gender. An average drink (say a 12 ounce can of some 5% ABV american lager), will contain about 0.6 fluid ounces of alcohol. A comparable amount of alcohol will be found in 1 shot (1.5 fl oz) of 40% liquor or a 5 ounce glass of 12% wine. My calculations for this can be found below, and show you will get drunk at a pace of 1 beer per hour if you are able to metabolize 0.25 fl oz.

Calculation of Amount of alcohol in a drink

BAC is determined by the amount of alcohol per amount blood. It is measured through your breathe, which has one tenth of the amount of alcohol as your blood. This means that if you blow a 0.10 BAC, your blood is actually 1% ABW (alcohol by weight). Blood consists of roughly 7% of a person's body weight, meaning a 170 pound man will have 11.9 pounds of blood. From the definition of BAC, we can solve for the weight of alcohol in a person at the legal threshold of .08%, and then find the volume of alcohol using it's density (.786 g/mL). The calculations, which are included below, show that the volume of alcohol in a 170 pound man who just blew a .08 is about 1.8 fl oz.

A BAC of .1 means there is 0.1 gram of alcohol in 100 gram of exhaled breath OR 1 gram of alcohol in each 100 gram portion of blood. We first need to find out how many 100g units of blood there are in the body. We will then have to multiply this number by the %ABW (which is 10 times the BAC) to find the grams of alcohol in the whole blood system. This can be converted to volume from the density of alcohol. We start by converting the weight of blood from pounds into grams.

We know that there are .8 grams of alcohol in each 100g section of blood. The number of grams in the 5.397 kg of blood can be found using cross multiplication.

Now that we know the weight of the total amount of alcohol in the body, we can use its density to find the volume and see how many beers it took to get there. Because we are working in metric, will we also have to convert the mL into fl oz in order to compare to the amount of alcohol in a single beer.

These calculations show that a 170 pound individual will have to have 1.84 fl oz of alcohol in his system to blow the .08. This is roughly equivalent to 3 beers, though the liver will be able to process some as he is drinking.

But back to the original question: What rate of beer consumption can the liver handle without becoming intoxicated?

Because each beer contributes 0.6 fluid ounces, and if liver is able to process 0.25 fluid ounces per hour, you would have to slow your consumption to a beer every 2.5 hours.

NOTE: The BAC analysis only accounts for the liver's contribution to clearing the alcohol from the body. Alcohol also leaves through your breathe, urine, and sweat. However, ,the majority of it (>85%) is processed by the liver. Another simplification I used was the method to calculate the amount of blood given someone's weight. This method of 7% of body weight was taken from the following book

Cameron, John R.; James G. Skofronick & Roderick M. Grant. Physics of the Body. Second Edition. Madison, WI: Medical Physics Publishing, 1999: 182.

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