A water cooler has the shape of a cylinder with height 80 cm and radius 40 cm. A

Question

A water cooler has the shape of a cylinder with height 80 cm and radius 40 cm. At the bottom is a valve of radius 4 cm from which water can flow. The outside air pressure can be approximated to be the same at the top and bottom of the cooler and equal to 1 atm. When the cooler is full, how fast does water exit the open valve initially? If we place our finger over the valve, what force is required to ensure no water flows out when the cooler is full? An electrical current flow without any resistance in a superconductor along its surface. If we think of a particular superconducting wire as an infinitely long, straight cylinder of radius 3 cm, then the current only flows along the surface of this cylinder (no current flows in the interior of the wire). Use Ampere's law to determine the following when the superconducting wire carries a 3.5 A current. What is the magnitude of the magnetic field inside the wire a distance 1 cm from its center? What is the magnitude of the magnetic field outside the wire a distance 7 cm from its center?

Explanation / Answer

16)

A) speed of efflux, v = sqrt(2*g*h)

= sqrt(2*9.8*0.8)

= 3.96 m/s

B) Area of the hole, A = pi*r^2

= pi*0.04^2

= 5.03*10^-3 m^2

pressure at the hole, P = Po + rho*g*h

= 1.013*10^5 + 1000*9.8*0.8

= 1.091*10^5 Pa

Force required, F = P*A

= 1.091*10^5*5.03*10^-3

= 549 N

17)

a) at r = 1 cm

B = mue*Iin/(2*pi*r)

= 0 (since there is no current inside)

b) at r = 7 cm = 0.07 m

B = mue*Iin/(2*pi*r)

= 4*pi*10^-7*3.5/(2*pi*0.07)

= 1.0*10^-5 T

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