Year 1 physics: Fluid Dynamics with Tree Sap replacing Water

AI Thread Summary
The discussion revolves around calculating the upward speed of tree sap in vessels, given a water loss of 110 g/h due to transpiration and the density of sap at 1040 kg/m³. The sap flow rate was converted to cubic meters per second, leading to a total volume needed to replace the lost water. The challenge lies in determining the speed of sap flow through each of the 1900 vessels, considering their diameter of 100 μm. There is uncertainty regarding whether the sap replacement should be calculated by weight or volume, although the density indicates a weight-based approach. The conversation emphasizes the need for clarity in the problem and encourages a deeper analysis of the calculations involved.
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Homework Statement


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 1900 vessels, each 100 μm in diameter, what is the upward speed of the sap in each vessel? The density of tree sap is 1040 kg/m3.

Known :
110g/hr water loss
d = 100μm
D = 1040kg/m^3

Homework Equations


berulinni's equation and contintuty equation :
p + 0.5*rho*v^2+rho*g*y = c
(v_1)(A_1) = (v_2)(A_2)

The Attempt at a Solution


Initially I converted the water loss to kg/s which was (110g/hr)*(1hr/3600seconds) and since 1 kg of water = 1L of water the water loss to be replaced by sap rate was 3.055*10^-5 m^3/s

Then calculated the volume of the sap to be 3.054x10-8 m^3 using Vsap=Vwater

Divided by vessels to get 1.60737*10^-11 m^3

And from now on, I only have uncertainties:
and a lot of possibilies but not sure how I can proceed.
 
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First of all, it is not clear from the question whether the water is replaced by weight or by volume. The fact that you are given the density of the sap suggests replacement by weight, although it will not matter much since the density is very similar to that of water.

Second, given that you have computed how much sap must flow through one vessel, how fast must it flow depending on the vessel diameter?
 
I am still stuck on this question if anyone could help out.
 
You have already gotten relevant comments, including a direct question. If you cannot answer this question, please state your thoughts on the matter and why this is not clear to you. If you are looking for someone to solve the problem for you you have come to the wrong place.
 
You're right, I didn't want to think about it. I will reattempt the question properly with your post in mind.
 

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