A water pipe having a 2.0 cm inside diameter carries water into the basement of

Question

A water pipe having a 2.0 cm inside diameter carries water into the basement of a house at a speed of 1 2 m/s and a pressure of 200,000 Pa. The pipe tapers to 1.0 cm inside diameter and rises to the second tor 7.0 m above the input point. (Density of water 1000 kg/m) a 6 points) Determine the water speed on the second floor. Answer (b) (8 points) Dctermine the water pressure on the second floor Answer (e) (7 points) If a person left a bath room tap running on the second floor for 30 minutes, what volume of water would exit the tap in that time?

Explanation / Answer

a] By continuity equation, A1v1 = A2V2

v1 pi*d1^2/4 = v2*pi*d2^2/4 because area = pi*d^2/4

v2 = v1 *(d1/d2)^2 = 1.2*(2/1)^2

= 4.8 m/s answer

b] Using Bernoullis equation, P1+ 0.5 rho v1^2 = P2 + rho v2^2 + rho g h

2e5 + 0.5*1000*1.2^2 = P2 +  0.5*1000*4.8^2 + 1000*9.8*7

P2 =  2e5 + 0.5*1000*1.2^2 - 0.5*1000*4.8^2 - 1000*9.8*7

= 120600 Pa answer

c] volume of water = Qt = v2A2 t = 4.8*pi*0.01^2/4 *30*60

= 0.6786 m^3 answer

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