Poiseuillé's law for the rate of flow of a fluid through a tube is a fourth-order polynomial that is also a power function: F = cR4, where F is the flow rate (measured as a volume per unit time), c is a constant, and R is the radius of the tube. (a) Assume that R increases by 10%. Explain why F increases by 46.41%. (Hint: Consider 1.10 raised to the fourth power.) If R increases by 10%, that means that R is multiplied by a factor of (round your answer to two decimal places). Since F is a power function with power , F changes by a factor of (round your answer to four decimal places), which is an increase of 46.41%. (b) What is the flow rate through a 1-inch pipe compared with that through a 1/2-inch pipe? (Round your answer to two decimal places.) times that in the 1/2-inch pipe (c) Suppose that an artery supplying blood to the heart muscle (see the figure above) is partially blocked and is only half its normal radius. What percentage of the usual blood flow will flow through the partially blocked artery? (Round your answer to two decimal places.)
Poiseuillé's law for the rate of flow of a fluid through a tube is a fourth-order polynomial that is also a power function: F = cR4, where F is the flow rate (measured as a volume per unit time), c is a constant, and R is the radius of the tube. (a) Assume that R increases by 10%. Explain why F increases by 46.41%. (Hint: Consider 1.10 raised to the fourth power.) If R increases by 10%, that means that R is multiplied by a factor of (round your answer to two decimal places). Since F is a power function with power , F changes by a factor of (round your answer to four decimal places), which is an increase of 46.41%. (b) What is the flow rate through a 1-inch pipe compared with that through a 1/2-inch pipe? (Round your answer to two decimal places.) times that in the 1/2-inch pipe (c) Suppose that an artery supplying blood to the heart muscle (see the figure above) is partially blocked and is only half its normal radius. What percentage of the usual blood flow will flow through the partially blocked artery? (Round your answer to two decimal places.)
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Poiseuillé's law for the rate of flow of a fluid through a tube is a fourth-order polynomial that is also a power function:
F = cR4,
where F is the flow rate (measured as a volume per unit time), c is a constant, and R is the radius of the tube.
(a) Assume that R increases by 10%. Explain why F increases by 46.41%. (Hint: Consider 1.10 raised to the fourth power.)
(b) What is the flow rate through a 1-inch pipe compared with that through a 1/2-inch pipe? (Round your answer to two decimal places.)
times that in the 1/2-inch pipe
(c) Suppose that an artery supplying blood to the heart muscle (see the figure above) is partially blocked and is only half its normal radius. What percentage of the usual blood flow will flow through the partially blocked artery? (Round your answer to two decimal places.)
%
If R increases by 10%, that means that R is multiplied by a factor of (round your answer to two decimal places). Since F is a power function with power , F changes by a factor of (round your answer to four decimal places), which is an increase of 46.41%.
(b) What is the flow rate through a 1-inch pipe compared with that through a 1/2-inch pipe? (Round your answer to two decimal places.)
times that in the 1/2-inch pipe
(c) Suppose that an artery supplying blood to the heart muscle (see the figure above) is partially blocked and is only half its normal radius. What percentage of the usual blood flow will flow through the partially blocked artery? (Round your answer to two decimal places.)
%
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