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20 April, 19:54

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?

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  1. 20 April, 20:22
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    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
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