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The velocity vector of a fluid is v=⟨x/z,y/z,0⟩ and it passes through a Cube C defined by 1≤x≤4,2≤y≤5,1≤z≤4. Let S be the boundary of this cube and calculate the flow rate of the fluid across S.
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- A helium balloon (in the shape of a sphere) has radius 7.10 m. For the density of air, please use 1.29 kg/m^3, and for Helium, use .179 kg/m^3 Part A How much additional mass (payload) could this balloon lift? You should assume the balloon's skin, plus other parts of the balloon's structure have a total mass of 900 kg. Note however that this number does NOT yet include the mass of the helium filling the balloon, which you will need to account for! Express your answer using two significant figures. ▸ View Available Hint(s) m = for Part A for Part A undo for Part A redo for Part A reset for Part A keyboard shortcuts for Part A help for Part A Submit Constants kgPoiseuillé'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…Gg