Year 1 physics: Fluid Dynamics with Tree Sap replacing Water

In summary, 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, the upward speed of the sap in each vessel is 1.60737*10^-11 m^3.
  • #1
ConquestAce
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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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  • #2
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
I am still stuck on this question if anyone could help out.
 
  • #4
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
You're right, I didn't want to think about it. I will reattempt the question properly with your post in mind.
 

1. What is fluid dynamics and why is it important?

Fluid dynamics is the study of how fluids (liquids and gases) behave when they are in motion. It is important because it helps us understand and predict the movement and behavior of fluids in various scenarios, such as in pipes, rivers, and the atmosphere. This knowledge is crucial for many industries, including engineering, meteorology, and oceanography.

2. Can tree sap really replace water in fluid dynamics experiments?

Yes, tree sap can be used as a substitute for water in fluid dynamics experiments. Tree sap is a fluid with similar properties to water, such as viscosity and density, making it a suitable substitute. It also has the advantage of being readily available and environmentally friendly.

3. How does using tree sap instead of water affect the results of fluid dynamics experiments?

The use of tree sap instead of water may slightly alter the results of fluid dynamics experiments. This is because tree sap has different properties than water, such as a higher sugar content, which may affect its viscosity. However, as long as the experiments are conducted with proper controls and comparisons are made with water-based experiments, the results can still be valid and useful.

4. What are some real-world applications of fluid dynamics with tree sap?

Fluid dynamics with tree sap can have various real-world applications. For example, it can be used to study the flow of tree sap through the xylem tubes of plants, which can provide insights into how trees transport water and nutrients. It can also be used to simulate the flow of sap in maple trees for maple syrup production, or in other industries that use tree sap as a raw material.

5. How can fluid dynamics with tree sap benefit the environment?

Using tree sap in fluid dynamics experiments can have several environmental benefits. As mentioned before, tree sap is a natural and environmentally friendly fluid, so its use can reduce the environmental impact of experiments. Additionally, studying the flow of tree sap can also provide insights into the health and functioning of trees, which can help in conservation efforts and monitoring of forest ecosystems.

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