Question

The old saying that you should wait at least 30 minutes after eating before you swim is based on the idea that after a big meal, blood will be diverted away from your arms and legs, towards your stomach’s digestive tract. And if your limbs don’t get enough blood flow to function, you’re at risk of drowning. With a reduced blood flow, there is potentially less oxygen available to the working muscle and stomach, which is a potential cause of cramping. Interestingly, there is no evidence for this, and the dangers of swimming after eating is widely believed to be a myth.

However, the added mass from a large meal can slightly affect a persons buoyancy. The effect of changing lung volume on submerged weight for the adult female population in fresh water is shown (taken from “Buoyancy and stability characteristics of the human body and personnel flotation devices” United States Coast Guard, 1970). Residual lung volume is the volume of air that remains in the lungs after maximum forceful expiration, functional residual volume is the volume of air present in the lungs at the end of passive expiration, and total lung volume is the volume of air contained in the lungs at the end of a maximal inspiration. The graph shows the difference between the buoyancy force of a person entirely submerged and the weight of the person as a function of percentile.

The equation of best fit for the buoyancy minus weight (assuming functional residual volume) at a given percentile is

−2.11 × (10^-5)y3 + 3.16 × (10^-3)y2 − 0.206y + 0.428

Assume that the we would want to remain afloat at the functional residual volume. If a person ate a 1 kg meal (the average person eats 2.5 kg per day in the US) then what fractional increase in power would be required for a person at a given percentile to stay afloat at the functional residual volume? Assume the person stays afloat by pushing down the water with their hands.

Note that swimming after eating is not a concern, and instead drinking and doing drugs is associ- ated more with drownings. Within the 18 to 34 age group 45% of all drownings are attributed to alcohol or drugs.

Question: If a person ate a 1 kg meal then what fractional increase in power would be required for a person at a given percentile of 60.8 percent to stay afloat at thw functional residual volume?

Answer 1

The difference in the bouyancy and the weight at a given percentile is given by the equation

this means that we would need that much force to keep us afloat, at a certain percentile.

At 60.8 percentile, the extra force required will be

When a person has had 1kg of food, that would mean that he would have an extra 1kg of weight.

So the

Now, the power is defined as the work done per unit time.

since the displacement will be the same for both the cases(that is with 1kg food and without 1 kg food), the power needed would be directly proportional to the force required.

Therefore, the fractional change in power would be

Here, we took the forces to be positive, as this much force is required to keep us afloat. In the earlier case, we got -ve value from that equation, because it was the difference between bouyant force and the weight and the negative sign indicated that we would sink if no force is applied.