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Q.59

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 386

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Short Answer

A tree loses water to the air by the process of transpiration at the rate of . This water is replaced by the upward flow of sap through vessels in the trunk. If the trunk contains 2000 vessels, each in diameter, what is the upward speed of the sap in each vessel? The density of tree sap is

Hence the speed of the vessel in each sap is

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Step by Step Solution

Step :1 Introduction 

The flow of a liquid through a pipe obeys the equation of continuity. When the water flows through a broader region, it has less velocity, and when it flows through a constricted region, it flows with higher velocity.

Step :2 Explanation 

The volume of fluid that crosses an area with speed in unit time is.

Convert the rate of mas of the fluid from :

Step : 3  Micro meter to  meter 

Convert the diameter of the vessel from micro meter to meter.

Radius of the vessel is,

Step :4  Mass of fluid 

Mass of the fluid is the product of volume of the fluid and density of the fluid

We can imagine there are many small tubes. Each will pass sap through a cross-section which will be lost to the air. Let be the area through which liquid pass with a speed . Then the rate with which the liquid mass passing through is:

Step :5  Volume of fluid

The volume of fluid that crosses an area with speed in unit time is given as

Now substitute in equation 1

Rearranging the above equation for velocity

Step:6 Area of vessel

Area of the vessel vessels is,

Substitute for density

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