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inna [77]
3 years ago
7

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?
Physics
1 answer:
Gnoma [55]3 years ago
7 0

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

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(A) 0.279N at angle 38.02°

(B) 0.701N

(C) 14.19°

Explanation:

(A) The net force on q3 is given as:

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Fy is the y component of the force

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Using SOHCAHTOA to find x,

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Where k = Coulumbs constant

F(1,3) = (k*q1*q3) / r²

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F(2,3) = (k*q2*q3) / r²

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Fy = 0.172N

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The magnitude of the force will be

F(mag) = √(0.22² + 0.172²)

F(mag) = 0.279N

The direction of the force makes will be

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θ = 38.02° to the x axis.

(B) q2 = - 2.0 * 10^(-6)

This implies that:

F(2,3) = (k*q2*q3) / r²

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(C) The direction of the force makes will be

tanθ = 0.172/0.68

θ = 14.19° to the x axis

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