(a) A water hose 4.00 cm in diameter is used to fill a 21.0 L bucket. If it take
ID: 1467994 • Letter: #
Question
(a) A water hose 4.00 cm in diameter is used to fill a 21.0 L bucket. If it takes 3.00 min to fill the bucket, what is the speed v at which water moves through the hose? (Note: 1 L = 1000 cm3.) cm/s (b) The hose has a nozzle 2.00 cm in diameter. Find the speed of the water at the nozzle. cm/s
Also, A plastic sphere floats in water with 30.0% of its volume submerged. This same sphere floats in an unknown fluid with 23.9% of its volume submerged. Determine the densities of the sphere and the unknown fluid. sphere kg/m3 fluid kg/m3
Explanation / Answer
(a) d1 =4 cm , r1 =2 cm, t =3 min
Volume V = 21 L = 21x1000 cm^3
Volume flow rate V/t = (21x1000)/(3x60) = 116.67 cm^3/s
Volume flow rate =A1v1
v1 = (V/t)/A1 = 116.67/(3.14x2x2) =9.289 cm/s
(b) d2 = 2cm , r2 = 1cm
Volume flow rate is constant A1v1 =A2v2
v2 = (A1/A2)v1 = (r1/r2)2v1 = (2/1)2(9.289)
v2 = 37.156 cm/s
Density o water dw = 1000 kg/m^3
From buoyancy force
weight of displaced WATER= weight of submerged sphere in water
dw(0.3V)g = ds (V)g
ds = (1000*0.3) =300 kg/m^3
weight of displaced LIQUID = weight of submerged sphere in LIQUID
dl(0.239V)g = ds (V)g
dl = (300)/0.239
dl = 1255.23 kg/m^3
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