In the Blasius equation stream function: j is a dímensionless plane p(x, y) f(n) VDUX Values of f are not given in Table 7.1, but one published value is f(2.0) = 0.6500. Consider airflow at 6 m/s, 20°C, and 1 atm past a flat plate. Atx= 1 m, estimate (a) the height y; (b) the velocity, and (c) the stream function at 7= 2.0. y[U/(vx)]!2 y[U/(vx)]!2 u/U u/U 0.0 0.0 2.8 0.81152 0.84605 0.87609 0.90177 0.92333 0.94112 0.2 0.06641 3.0 0.4 0.13277 3.2 0.6 0.19894 3.4 0.8 0.26471 3.6 1.0 0.32979 3.8 1.2 0.39378 4.0 0.95552 1.4 0.45627 4.2 0.96696 1.6 0.51676 4.4 0.97587 1.8 0.57477 4.6 0.98269 2.0 0.62977 4.8 0.98779 2.2 0.68132 5.0 0.99155 2.4 0.72899 1.00000 2.6 0.77246

A- Womersley number (a) of a human aorta is 20 and for the rabbit aorta is 17, the blood density is approximately the same across the species. The values of viscosity were 0.0035 Ns/m² for the human and 0.0040 Ns/m² for the rabbit. The diameter of the aorta is 2.0 cm for the man, and 0.7 cm for the rabbit, estimate the heart rate beats per minute (bpm) for both species

The Keystone Pipeline opener photo hasD = 36 in. and an oil flow rate Q = 590,000 barrels per day(1 barrel = 42 U.S. gallons). Its pressure drop per unitlength, ∆p/L , depends on the fluid density ρ , viscosity μ ,diameter D , and flow rate Q . A water-fl ow model test, at20 ° C, uses a 5-cm-diameter pipe and yields ∆ p/L ≈ 4000Pa/m. For dynamic similarity, estimate ∆ p/L of the pipeline.For the oil take ρ = 860 kg/m 3 and μ = 0.005 kg/m . s.

The true option

A milkshake has fairly similar density to that of water (m s = 1200 kg/m3) but is far more viscous ( = 1kg/m
s) (a) Say you try to drink a milkshake through a straw that is 30 cm long and 5 mm in diameter. Your lungs are capable of creating a vacuum pressure of 3000 Pa. (Vacuum pressure just means a pressure below that of the atmosphere, so plung = patm  3000 Pa.) You Önd that if you place the straw just at the surface of the liquid, you are unable to suck the milkshake through the straw, but if you push the straw deeper into the shake, you can. To what depth, d, would you need to push the straw in order to just start to sip the milkshake?(b) Suppose you push the straw to a depth of 10 cm and suck with a suction pressure of 3000 N/m2. What volume áow rate of milkshake can you produce through the straw

Problem 4: The power P developed by a wind turbine is a function of diameter D, air density p, wind speed V, and rotational rate @. Viscous effect is negligible. (4a) Rewrite the above relationship in a dimensionless form; (4b) In a wind tunnel, a small model with a diameter of 90cm, rotating at 1200 RPM (revolution per minute), delivered 200 watts when the wind speed is 12m/s. The data are to be used for a prototype of diameter of 50m and wind speed of 8 m/s. For dynamic similarity, what will be (i) the rotational speed of the prototype turbine? (ii) the power delivered by the prototype turbine? Assume air has sea-level density.