Question

CHE 3315 FLUID MECHANICS PROBLEM SHEET 5: MASS CONSERVATION AND FLOW RATE 1. Determine the mass flow rate of air having a temperature of 20C and gauge pressure 80 kPa as it flows through a circular duct 400 mm in diameter with an average velocity of 3 m/s. The gas specific constant R 286.9 JK /kg 2. Determine the average velocity of the steady flow at one outlet of a T- junction if the inlet flow speed is 6 m/s (diameter 0.1 m) and the other outlet is 2 m/s (diameter 0.05 m). The outlet diameter of interest is 0.1 m.

Answer 1

Concept required- the mass flow rate is given by the formula -

Concept required - the mass flow rate is given by the formula - PV = mRT where - P = total pressure, V = volume, m = mass flow rate, R = gas constant, T = temperature Part a - Given - temperature = 20C = 293 K Total pressure, P = absolute pressure + gauge pressure = 1.01325 + 0.8 = 1.81325 bar Diameter = 400 mm = 0.4m velocity = 3 m/s R = 286.9 J. K /kg Area = pi D^2/4 = 3.14 times 0.4^2/4 = 0.1256m^2 Volume = area times velocity = 0.3769 m^3/s using - PV = mRT 1.81325 times 10^5 *0.3769 = m*286.9*293 0.6834 times 10^5 = m*84061.7 0.6834 times 10^5/84061.7 = m = 0.81299kg/s Thus the mas flow rate is 0.81299 kg/s

where - P = total pressure , V = volume , m = mass flow rate , R = gas constant , T = temperature

Solution

Part a -

Given -

temperature =20C = 293 K

Total pressure , P= absolute pressure + gauge pressure = 1.01325 + 0.8 = 1.81325 bar

Diameter = 400 mm = 0.4m

velocity = 3 m/s

R = 286.9 J. K /kg

Volume = area X velocity = 0.3769 m³ / s

using  -

Thus the mas flow rate is 0.81299 kg/s