Question

Chloroform flows through a 4.26 inch inside-diameter pipe at the rate of 3.60 gallons per minute. What is the average velocity of chloroform in the pipe? Number ft/s The specific gravity of chloroform is 1.49. What is the mass flow rate of the liquid for the conditions described above?

Answer 1

Answer:

1) 0,081 ft/s

2) 0,746 lb/s

Explanation:

The relation between flow and velocity of a fluid is given by:

Q=Av

where:

• Q, flow [ft3/s]
• A, cross section of the pipe [ft2]
• v, velocity of the fluid [ft/s]

1)

To convert our data to appropiate units, we use the following convertion factors:

1 ft=12 inches

1 ft3=7,48 gallons

1 minute=60 seconds

So,

$Q=\frac{3,60 gallons}{1 min}*\frac{1min}{60 s}*\frac{1ft3}{7,48gallons}=0,00802 \frac{ft3}{s}$

As the pipe has a circular section, we use A=πd^2/4:

$d=4,26 inch *\frac{1ft}{12 inch}=0,355ft\\ A=\pi \frac{0,355^{2} }{4}=0,0989ft2$

Finally:

Q=vA......................v=Q/A

$v=\frac{0,00802ft^{3} /s}{0,0989ft^{2} }=0,081ft/s$

2)

The following formula is used to calculate the specific gravity of a material:

SG = ρ / ρW  

where:

• SG = specific gravity,

• ρ = density of the material [lb/ft3]

• ρW = density of water [lb/ft3] = 62.4 lbs/ft3

then:

ρ = SG*ρW   = 1,49* 62,4 lb/ft3 = 93 lb/ft3

To calculate the mass flow, we just use the density of the chloroform in lb/ft3 to relate mass and volume:

$0,00802 \frac{ft3}{s}*\frac{93lb}{1ft3}=0,746lb/s$