A main water line is used to supply water to 50 houses. The
diameter of the line is 6 inches and water flows through the line at a
rate of 550 gal/min. If an equal volume of water flows into each of
the houses, determine the velocity of the water in m/s and the mas
flow rate in kg/s in a 1" diameter pipe going into a house. Use a
density of water of 998 kg/m3, 1 gal=3.788 L, 1 L=10-3 m3, 1 in=2.54
cm.
Solution.
"n=50;"
"D=6\\sdot2.54cm=15.24cm=0.1524m;"
"v=550\\sdot3.788L\/min=2.08m^3\/min=0.035m^3\/s;"
"D_1=2.54cm=0.0254m;"
"\\dfrac{S}{nS_1}=\\dfrac{v_1}{v}\\implies v_1=\\dfrac{Sv}{nS_1}" ;
"v_1=\\dfrac{D^2\\sdot v}{D_1^2\\sdot N};"
"v_1=\\dfrac{0.1524^2\\sdot0.035}{50\\sdot0.0254^2}=0.025m^3\/s;"
"m=V\\sdot\\rho;"
"m_1=0.025\\sdot998=24.95kg\/s;"
Answer: "v_1=0.025m^3\/s; m_1=24.95kg\/s."
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