The leaves of a tree lose water to the atmosphere via the process of transpiration. A particular tree loses water at the rate of 3 x 10^-8 m^3/s; this water is replenished by the upward flow of sap through vessels in the trunk. This tree's trunk contains about 2000 vessels, each 100Mu m in diameter. What is the speed of the sap flowing in the vessels?

The speed of the sap flowing in the vessel is 1.90 mm/s

Explanation:

Given:

The rate of water loss, Q = 3 * 10 ⁻⁸ m³/s

Number of vessels contained, n = 2000

Diameter of the vessel, D = 100 Mu m

thus, the radius of the vessel, r = 50 * 10⁻⁶ m

Now, the rate of flow is given as:

Q = AV ... (1)

where, A is the area of the cross-section

V is the velocity

Total area, A = n * (πr²)

substituting the values in the equation (1), we get

3 * 10 ⁻⁸ m³/s = [2000 * (π * (50 * 10⁻⁶) ²) ] * V

or

V = 1.909 * 10⁻³ m/s or 1.90 mm/s

Hence, the speed of the sap flowing in the vessel is 1.90 mm/s