Question

Question: (a) What is the order of magnitude of the number of microorganisms in the human intestinal tract? A typical bacterial length scale is 10^-6. Estimate the intestinal volume and assume 1% of it is occupied by bacteria. (b)Does the number of bacteria suggest whether the bacteria are beneficial, dangerous, or neutral for the human body? What functions could they serve?

Short answer

Answer

1. The volume of intestine is $34.1\times {10}^{-4}{m}^3$.

2. There are so many bacteria that it is likely that they are helpful; some types of bacteria in the digestive tract are good for you since they facilitate digestion and stop harmful bacteria from growing in the intestines

Step-by-step solution

Identify given data

Scale of bacteria is$d_{bac}={10}^{-6}m$ .

The volume occupied by bacteria is 1% of volume of intestine.

(a) Determine the volume of human intestinal tract

The capacity of large intestine is 1.45 litres on average (Olle Olsson (1952): The Capacity of the Large Intestine).

$V_{l\arg e}=1.45litres=14.5\times {10}^{-4}{m}^3$

Intestinal tract can be approximated as a cylinder. The average length of the small intestine is and average diameter is ; therefore, the volume of the small intestine is

$$\begin{gathered} V_{small}=\frac{\pi }{4}{d}_{small}^{2}L \\ =\frac{\pi }{4}{\left(2.5\times {10}^{-2}m\right)}^2\left(4m\right) \\ =19.6\times {10}^{-4}{m}^3 \end{gathered}$$

Therefore, the total volume of the intestinal tract is

role="math" $$\begin{gathered} V_{int}=V_{small}+V_{l\arg e} \\ =19.6\times {10}^{-4}{m}^3+14.5\times {10}^{-4}{m}^3 \\ =34.1\times {10}^{-4}{m}^3 \end{gathered}$$

Determine the number of bacteria in intestine

The volume occupied by bacteria is 0.01 times that of the whole volume of the intestine.

$$\begin{gathered} V_{bac}=0.01V_{int} \\ =0.01\left(34.1\times {10}^{-4}m\right) \\ =0.34\times {10}^{-4}m \end{gathered}$$

Let’s assume that the shape of bacteria is spherical with diameter of 10^-6, therefore the volume of one bacterium is

$$\begin{gathered} {V\text{'}}_{bac}=\frac{4}{3}\pi {\left(\frac{d}{2}\right)}^3 \\ =\frac{4}{3}\pi {\left(\frac{{10}^{-6}m}{2}\right)}^3 \\ =0.52\times {10}^{-18}m \end{gathered}$$

Therefore, the number of bacteria is

$$\begin{gathered} \frac{V_{bac}}{{V\text{'}}_{bac}}=\frac{0.34\times {10}^{-4}{m}^3}{0.52\times {10}^{-18}{m}^3} \\ =0.65\times {10}^{14} \end{gathered}$$

(c) Since there are so many bacteria, it is likely that they are helpful; if they weren't, the body would have long since devised strategies to lessen their population. It is generally known that some types of bacteria in the digestive tract are good for you since they facilitate digestion and stop harmful bacteria from growing in the intestines.