a)To water the yard, you use a hose with a diameter of 2.7 cm. Water flows from

Question

a)To water the yard, you use a hose with a diameter of 2.7 cm. Water flows from the hose with a speed of 1.4 m/s. If you partially block the end of the hose so the effective diameter is now 0.55 cm, with what speed does water spray from the hose?
?m/s

bTo fill a child's inflatable wading pool you use a garden hose with a diameter of 2.8 cm. Water flows from this hose with a speed of 1.1 m/s. How long will it take to fill the pool to a depth of 27 cm if it is circular and has a diameter of 3.3 m?
?min

Explanation / Answer

a) The diameter of hose at first end, d1 = 2.7 cm = 0.027 m So the area of hose at first end, A1 = (d1/2)^2 = 5.7 * 10^-4 m^2 The speed at first end, V1 = 1.4 m/s The deameter of hose at second end, d2 = 0.55 cm = 0.0055 m So the area of hose at second end, A2 = (d2/2)^2 = 2.4 * 10^-5 m^2 Let the speed at the second end of the hose = V2 We have an equation from the equation of continuity as            A2V2 = A1V1 From the above we have            V2 = A1V1 / A2 = 33.25 m/s So the speed of water spray at the second end of the hose is 33.25 m/s b) The diameter of hose, D = 2.8 cm = 0.028 m depth od pool, h = 27cm = 0.27 m
Volume of pool v = h*s = 0.27 * * (3.3^2)/4 = 2.31 m^3 we ahve v' = L**(0.028^2)/4 = 2.31    => L = 37007 m => t = 37007 / 1.1 = 33642 sec

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