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Manning’s Equation Hydrologists sometimes use Manning’s equation to calculate the velocity
For a certain brass pipe, the roughness coefficient has been measured to be
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Chapter P Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Flow Speed in a Channel The speed of water flowing in a channel, such as a canal or river bed, is governed by the Manning Equation, V=1.486A2/3S1/2p2/3n Here V is the velocity of the flow in ft. /s; A is the cross-sectional area of the channel in square feet: S is the downward slope of the channel; p is the wetted perimeter in feet (the distance from the top of one bank, down the side of the channel, across the bottom, and up to the top of the other bank); and n is the roughness coefficient (a measure of the roughness of the channel bottom). This equation is used to predict the capacity of flood channels to handle runoff from heavy rainfalls. For the canal shown in the figure, A=75ft2 , S=0.050 , p=24.1ft and n=0.040 . (a) Find the speed at which water flows through the canal. (b) How many cubic feet of water can the canal discharge per second? [Hint: Multiply V by A to get the volume of the flow per second.].arrow_forwardFlow Speed in a Channel The speed of water flowing in a channel, such as a canal or river bed, is governed by the Manning Equation, V=1.486A2/3S1/2p2/3n Here V is the velocity of the flow in ft/s; A is the cross-sectional area of the channel in square feet; S is the down-ward slope of the channel; p is the wetted perimeter in feet the distance from the top of one bank, down the side of the channel, across the bottom, and up to the top of the other bank; and n is the roughness coefficient a measure of the roughness of the channel bottom. This equation is used to predict the capacity of flood channels to handle runoff from heavy rainfalls. For the canal shown in the figure, A=75ft2,S=0.050,p=24.1ft, and n=0.040. a Find the speed at which water flows through the canal. b How many cubic feet of water can the canal discharge per second? Hint: Multiply V by A to get the volume of the flow per secondarrow_forwardHubbles Constant Astronomers believe that the universe is expanding and that stellar objects are moving away from us at a radial velocity V proportional to the distance D from Earth to the object. a. Write V as a function of D using H as the constant of proportionality. b. The equation in part a was first discovered by Edwin Hubble in 1929 and is known as Hubbles law. The constant of proportionality H is known as Hubbles constant. The currently accepted value of Hubbles constant is 70 kilometers per second per megaparsec. One megaparsec is about 3.0861019 kilometers. With these units for H, the distance D is measured in megaparsecs, and the velocity V is measured in kilometers per second. The galaxy G2237+305 is about 122.7 megaparsecs from Earth. How fast is G2237+305 receding from Earth? c. One important feature of Hubbles constant is that scientists use it to estimate the age of the universe. The approximate relation is y=1012H Where y is time in years. Hubbles constant is extremely difficult to measure, and Edwin Hubbles best estimate in 1929 was about 530 kilometers per second per megaparsec. What is the approximate age of the universe when this value of H is used? d. The calculation in part c would give scientists some concern, since Earth is thought to be about 4.6 billion years old. What estimate of the age of the universe does the more modern value of 70 kilometers per second per megaparsec give?arrow_forward
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