(2a). A substance flows through a 2 in diameter pipe with an average velocity of
ID: 2997966 • Letter: #
Question
(2a). A substance flows through a 2 in diameter pipe with an average velocity of 4 ft/s at a particular location.
Determine the mass flow rate, in lb/s, if the substance is:
(a) Water at 80 oF and 0.4 psia.
(b) Nitrogen as an ideal gas at 0.4 psia, 80 oF.
(2c). The conservation of mass and conservation of energy are well known principles in thermpdynamics, please explain if there is a universal conservation of volume principle. In what kind of process the volume is conserved?
(3). Steam enters a well-insulated, horizontal nozzle operating at steady state with a velocity of 10 m/s. If the specific enthalpy decreases by 45 kJ/kg from inlet to exit, determine the velocity at the exit, in m/s.
(6). A steadily operating heat exchanger is used to cool the hot water using liquid water from river. Hot water enters this heat exchanger at 0.1 bar and quality of 0.9, and a mass flow rate of 10 kg/s, and exits at 0.1 bar as saturated liquid water. The cooling water enters this heat exchanger at 15 oC and leaves at 35 oC. Ignoring the heating transfer from heat exchanger to ambient air, please find the mass flow rate of cooling water, in kg/s.
Explanation / Answer
2a)
Cross-section area A = pi/4*d^2
= 3.14/4 *2^2
= 3.14 in^2
= 3.14/12^2 ft^2
= 0.0218 ft^2 = 0.002026 m^2
a)
From water properties at 80 deg F and 0.4 psia we get, specific volume v = 803 ft^3/lb
Mass flow rate = A*V/v
= 0.0218*4/803
= 1.0862*10^-4 lb/s
b)
Density = P/(RT)
For nitrogen gas constant R = 297 J/kg-K
We have P = 0.4 psia = 2758 Pa
T = 80 deg F = 300 K
Density = 2758 / (297*300) = 0.031 kg/m^3
V = 4 ft/s = 1.22 m/s
Mass flow rate = Density*A*V
= 0.031*0.002026*1.22
= 7.65*10^-5 kg/s
= 1.687*10^-4 lb/s
2c)
Volume will be conserved when density will be conserved. Or in other words the fluid is incompressible.
3)
h1 + V1^2 /2 = h2 + V2^2 /2
h1
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