Conversion of flow quantities by the continuity equation water flows through a 3-inch, schedule 40 steel pipe (inside diameter- 3.068 inches) with an average velocity of 4 ft/s. compute: (a) mass flow rate in lb/h, (b) volumetric flow rate in ft /h, and (c) mass velocity (mass flux) in lb/h-ft.

a) m  = 2398256.64 Ib/hr

b) Q = 38433.6 ft^3/hr

c) J = = 898560 lb/h-ft2

Explanation:

a) To get the mass flow rate in lb/h we are going to use this formula:

m = ρνA

note: we have to change some units to reach to the final units

when m is the mass flow rate which we need to calculate

ρ is the density of water in lb/ft3 = 62.4 lbs/ft3 it is a constant numbers you can get it from anywhere

ν is the velocity of the water = 4 ft/s we need to change it to ft/h unit so  

when 1 ft/s = 3600 ft/hr (note : 3600 is a result of converting hr to sec 60min*60sec)

so  the velocity of the water = 4 ft/s * 3600 ft/hr= 14400 ft/hr

now , we need to get the area of the pipe in feet also when:

A = π*diameter * length

diameter = 3.068 inches

when 1 inch = 0.0833333333 feet so,

diameter in feet = 3.068 * 0.0833333333 =.300 0.2557ft

and length = 40 * 0.0833333333  = 3.333 ft

so the area of the pipe in feet^2 = 3.14*0.255*3.33 =2.669 ft^2

by substitution in the mass flow rate:

m = 62.4 lbs/ft3 * 14400 ft/hr *2.669 ft^2 = 2398256.64 Ib/hr

b) now to calculate volumetric flow rate in ft /h  we are going to use this formula:

Q = AV

when Q is  the volume flow rate

A is the cross-sectional area filled by water =2.669 ft^2

V is the average velocity of the water = 14400 ft/hr

so , by substitution:

Q = 2.669  ft^2* 14400 ft/hr= 38433.6 ft^3/hr

C) To calculate mass velocity (mass flux) in lb/h-ft  we are going to use this formula:

J = m / A

when J is the mass flux

and m is the mass flow rate which we calculated above = 2398256.64 Ib/hr

and A is the cross section area of the pipe which we calculated above and = 2.669 ft^2

so, by substitution:

J = 2398256.64 Ib/hr /  2.669 ft^2

 = 898560 lb/h-ft2

your parents i think this could be it

b is the correct answer

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