A tree loses water to the air by the process of transpiration at the rate of 110 g/h. This water is replaced by the upward flow of sap through vessels in the trunk. If the trunk contains 2000 vessels, each 100 mm in diameter, what is the upward speed of the sap in each vessel? The density of tree sap is 1040 kg/m3.

The answer is 1.87nm/s.

Explanation:

The  water loss must be replaced by of sap. 110g of sap corresponds to a volume of  

thus rate of sap replacement is

The volume of sap in the vessel of length is

,

where is the cross sectional area of the vessel.

For 2000 such vessels, the volume is

taking the derivative of both sides we get:

on the left-hand-side is the velocity of the sap, and on right-hand-side ; therefore,

and since the cross-sectional area is

;

therefore,

solving for we get:

which is the upward speed of the sap in each vessel.

it is given that trillions of microbes make up to 1% to 3% of the body mass.

let's take average of this percentage: 2%

consider the average mass of the human body as 70 kg.

then, trillions of microbes would have mass  

therefore, 100 trillion micro-organisms would weigh:

this is an approximate value and could change depending on the mass of the human body and percentage of the microbes present in it.

average mass per microorganism =