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.

the answer is 46 mls because when you add the speed per second it increses the speed

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