Question

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?

Answer 1

Answer:

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

Answer 2

The speed of the sap flowing in the vessels is $1.91 \times 10^{-3} \ m/s$.

Continuity Equation

The speed of the sap flowing in the vessels is calculated by applying continuity equation.

The given parameters:

• Number of vessels, n = 2000
• Diameter, d = 100μ m
• Radius, r = 50μ m
• Flow rate,  Q = 3 x 10⁻⁸ m³/s

The speed of the sap flowing in the vessels is calculated as;

$Q = n(Av)\\\\v = \frac{Q}{nA} \\\\v = \frac{3 \times 10^{-8}}{2000 \times \pi (50 \times 10^{-6})^2} \\\\v = 1.91 \times 10^{-3} \ m/s$

Learn more about flow rate here: https://brainly.com/question/21630019