Answer to Question #218034 in Mechanics | Relativity for Sammy

Question

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.

Answer 1

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: $v_1=0.025m^3/s; m_1=24.95kg/s.$