Answer:
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
