For this problem use: ?water = 1000 kg/m3 A cylindrical water-storage tank has a

Question

For this problem use: ?water = 1000 kg/m3
A cylindrical water-storage tank has a height of 8.1 m and a radius of 6.2 m. The storage tank is full of water but is vented to the atmosphere. The bottom of the tank is 35 m off the ground. A 12 cm diameter pipe runs vertically down from the tank and goes 2.0 m underground before turning horizontal. The water flow in the horizontal pipe is 85 L/s.

A) What is the water pressure in the horizontal pipe underground? (kPa)

B) How fast does the water level in the tank drop? (mm/s)

C) Someone drills a 6.8 mm diameter hole near the bottom of the tank. How fast does the water shoot out? (m/s)

D) What volume flow of water is lost out the hole? (L/s)

Explanation / Answer

let v be flow speed. v*pi*6e-2^2=85e-3 so v=7.5(m/s). -------- so bernulli equation. P0+D*g*35=P+Dv^2/2-D*g*2 so that P=4.34e5(Pa) ------------ it is 85e-3/pi*6.2^2=0.7e-3(m)=0.7(mm) -------- it is v=sqrt(2*9.8*8.1)=12.6(m/s) --------- it is 12.6*3.4e-3^2*pi=4.57e-4(m3/s)=4.57e-1(L/s)

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