A stream U In the x-direction has components o = U cos@and vg -U sin 0. The stream function of the flow Is glven by 00

(a) Assuming that each cubic centimeter of water has a mass of exactly 1 g, find the mass of 8.88 cubic meter of water. (b) Suppose that it takes 15.5 hours to drain a container of 87.0 m3 of water. What is the "mass flow rate," of water from the container?

The Ekman number, Ek, arises in geophysical fluid dynamics. It is dimensionless parameter combining seawater density ρ, a characteristic length L, Seawater viscosity μ, and the Coriolis frequency Ωsinφ, where Ω is the rotation rate of the earth and φ is the latitude angle. Determine the correct form of Ek if the viscosity is in the numerator.

(a) Estimate the time it would take (in hours) to fill a private swimming pool with a capacity of 90,000 L using a garden hose delivering 39 L/min. hours (b) How long would it take (in s) to fill if you could divert a moderate size river, flowing at 2200 m/s, into it?

A cylinder was measured to have length 4.24 + 0.01 cm and diameter of thecross-sectional area 2.16 + 0.01 cm. Find its volume and the percentageuncertainty ΔV/V.

show that v^2/r has dimensions of m/s^2

(a) Assuming that each cubic centimeter of water has a mass of exactly 1 g, find the mass of 8.70 cubic meter of water. (b) Suppose that it takes 15.0 hours to drain a container of 39.4 m3 of water. What is the "mass flow rate," of water from the container?

a) Write down the metric and the inverse metric, and use the definitionrpµv = 1/2gpσ(δµgvσ + δvgµσ - δσgµv) = rpvµto reproduce the results written above for rθ ØØ and rØ θØ.