# Year 1 physics: Fluid Dynamics with Tree Sap replacing Water

1. Oct 26, 2015

### ConquestAce

1. The problem statement, all variables and given/known data
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

2. Relevant 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)

3. 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.

2. Oct 26, 2015

### Orodruin

Staff Emeritus
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?

3. Nov 1, 2015

### ConquestAce

I am still stuck on this question if anyone could help out.

4. Nov 1, 2015

### Orodruin

Staff Emeritus
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.

5. Nov 1, 2015

### ConquestAce

You're right, I didn't want to think about it. I will reattempt the question properly with your post in mind.