ENG 201 Lecture, Spring 2012

9-0 CHAPTER 9 Mass and Mass-Related Parameters 9-1 9-2 Mass - derived parameters • Density = mass/volume • Specific gravity = density/density of water at 4oC • Specific volume = volume/mass = 1/ density • Specific weight = weight/volume = density * g (g = acceleration due to gravity) 9-3 9-4 9-5 Volume flow rate • Engineers design flow-measuring devices to determine the amount of material or a substance flowing through a pipeline in a processing plant. • They calculate it by: Volume flow rate = volume/time = area x length/time = area x (average velocity) The latter formula is practically simpler to determine • Common units are: m3/s, m3/h, L/s, ml/s, ft3/s (cfs), gal/min (gpm), gal/day (gpd) 9-6 9-7 Example • What is the volume flow rate of the water in the piping system? Express the answer in ft3/s, gpm and L/s. what is the average speed of water in the 6-in diameter pipe? 9-8 Example 9-9 Mass flow rate • Mass flow rate = (displaced mass)/time = (volume/time)(mass/volume) = volume flow rate * density 9-10 Mass moment of inertia • It is a measure of how hard it is to rotate something (with respect to its center of rotation) • I z-z = m r2 9-11 Mass moment of inertia • I z-z = m1 r1 2 + m2r2 2 + m3r3 2 9-12 • For a body of any shape: • I z-z = ∫r2dm Mass moment of inertia 9-13 9-14 9-15 9-16 Example 9.1 • Determine the mass moment of inertia of a steel shaft (around its axis) that is 2m long and has a diameter of 10 cm. the density of steel is 7860kg/m3. • Answer: 0.154Kg m2 9-17 Momentum • L = m V • A man of mass 70 Kg running at 10m/s has a momentum of 700 Kg m/s → → 9-18 Momentum • A bullet moving at 1000m/s, having a mass of 4g. Its momentum is 4Kg m/s • It has a high momentum due to its speed. That is why it can penetrate objects and do harm. (This is also due to its small contact area) 9-19 Example 9.2 • Compare linear momentum of : – Person 80 kg ; 3m/s – Car 2000 kg ; 30 m/s • Answer: – Person: 240 kg m/s – Car : 60 000 kg m/s 9-20 Conservation of mass • Rate of accumulation = rate of fluid – rate of fluid of fluid entering leaving 9-21 Example 9.3 • How much water is stored after 5 min in each of the tanks? How long will it take to fill the tanks? 9-22 Example 9.3 • Density of water 1000kg/m3 • Tank 1: – rate of water entering 2 kg/s – Volume of tank: 12 m3 • Tank 2: – rate of water entering 2 kg/s – Volume of tank: 12 m3 – Rate of water leaving :1 kg/s