We jump ahead to modern times and find Lazydog having lunch at Shoney\'s. While

Question

We jump ahead to modern times and find Lazydog having lunch at Shoney's. While pounding down a BBQ bacon cheeseburger (only 1470 calories and 49 fat grams), the good professor worked on the following problems. Grab yourself an 875 calorie Ultimate Hot Fudge Cake from Shoney's and help the prestigious professor solve these problems.

A.The honored Lazydog fondly recalls the many times he has sliced a golf ball into the water. This leads him to decide to calculate the terminal velocity in water of a 4.0 cm diameter ball that has a specific gravity of 1.08. Assume the viscosity of water is 1.0x10-3 Pas. What do you calculate as the terminal velocity of this ball in water?

(include units with answer)

B.The distinguished Lazydog now decides to calculate how long it would take to drain a 2.5 ft wide by 6.0 ft long bathtub from full to half full. The initial height of the water in the tub is 2.3 ft and the water goes out a 2.6 inch diameter drain in the bottom of the tub.

(include units with answer)

C.The celebrated Lazydog has recently added a 64 m3workshop on to his house. What diameter must a 4 m long air duct have if the heating and air conditioning system is to replenish the air in the room every 15 minutes? The pump can exert a gage pressure of 0.86x10-3 atm. Assume atmospheric pressure is 101.3 kPa and the viscosity of air is 0.018x10-3 Pas.

(include units with answer)

Explanation / Answer

From the given data

A. diameter, d = 0.04 m

specific gravity, rho' = 1.8

nu = 10^-3 Pa s

Terminal velocity = 2*1000(rho' - 1)g*d^2/36*nu ( from stokes law)

hence

vt = 697.6 m/s

B. given

width w = 2.5 ft

length l = 6 ft

hi = 2.3 ft

hf = 1.15 ft

d = 2.6 in

hence

at time t

speed of flow from the pipe = v

v = sqroot(2gh)

also, rate of volume change

dV/dt = rho*pi*d^2*v/4

now, V = wl*h

hence

dh/dt = rho*pi*d^2*sqroot(2gh)/4*wl = 0.03826727*sqroot(h)

hence

dh/sqroot(h) = 0.03826727*dt

integrating

2*sqroot(h) = 0.03826727t + c

at t = 0, h = 2.3 ft

hence

c = 3.033

hence

at h = 1.15 ft

t = 23.378661 s

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