The circular stream of water from a faucet is observed to taper from a diameter of 20 mm to 10 mm in a distance of 50 cm. determine the flowrate.

Solution:

From Bernoulli equation

ρ + ρgh = ρ , where ρ is density of water, h – height difference and and  are the velocities in upper and lower cross sections correspondingly. We take into account that the pressure in both cross-sections is the same and equal to the atmospheric one.

From the continuity and assuming water incompressible:

= , where and are the corresponding cross-sections. As the lower diameter is twice as low as the upper one, we can conclude that

Inserting it back into Bernoulli equations produces:

and the flow rate is

-22

times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3

answer would be 8.64 or s = 11π/4 inches

step-by-step explanation:

s = r θ  

where s = arc length  

r = radius = 3 inches  

θ = central angle in radians = ( π /180)*165  

s = 3(π/180)*165  

= 8.64 inches