Question

Water flows from the mains to the plumbing of a house. The house pipes have a radius of 3.6 cm and the water flows through them at a velocity of 0.14 m/s. Calculate the maximum velocity (in m/s) of water that can be obtained from a tap that has been fully opened where the tap radius is 0.8 cm.

A square metal plate of length 1.1 m is lying on the ground in the direct sunlight on a hot day and its temperature rises to 65 degrees Celsius. If the plate has an emissivity of 0.8, what net power (in W) is radiated from the plate if the air temperature is 48 degrees Celsius?

Answer 1

1) v1 = 0.14 m/s

r1 = 3.6 cm

r2 = 0.8 cm

using equation of continuity

A1v1 = A2V2

pi * r1^2 * v1 = pi * r2^2 * v2

(3.6)^2 * 0.14 = (0.8)^2 * V2

v2 = 2.835 m/s

Therefore, maximum velocity = 2.835 m/s

2) Net power = e A [(T1)^4 - (T2)^4]   ..(Stefan's law)

Net power = 5.67 * 10^ (-8) * 0.8 * (1.1*1.1) [(65+273)^4 - (48+273)^4]

Net power = 133.6 Watts

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