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
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.
The volume of fluid that crosses an area with speed in unit time is.
Convert the rate of mas of the fluid from :
Convert the diameter of the vessel from micro meter to meter.
Radius of the vessel is,
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:
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
Area of the vessel vessels is,
Substitute for density
Glycerin is poured into an open U-shaped tube until the height in both sides is . Ethyl alcohol is then poured into one arm until the height of the alcohol column is . The two liquids do not mix. What is the difference in height between the top surface of the glycerin and the top surface of the alcohol?
Geologists place tiltmeters on the sides of volcanoes to measure the displacement of the surface as magma moves inside the volcano. Although most tiltmeters today are electronic, the traditional tiltmeter, used for decades, consisted of two or more water-filled metal cans placed some distance apart and connected by a hose. FIGURE shows two such cans, each having a window to measure the water height. Suppose the cans are placed so that the water level in both is initially at the mark. A week later, the water level in can is at the mark.
A. Did can move up or down relative to can ? By what distance?
B. Where is the water level now in can ?
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