Process fluid flow PFF, Lecture notes of Fluid Dynamics

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Process Fluid Flow (PFF260S)

3.13 Conservation of Momentum

• Newton’s second law of motion for a system is: 𝑇𝑖𝑚𝑒 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑖𝑛𝑒𝑎𝑟 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚

• Time rate of change of the linear momentum = 𝐷 𝐷𝑡

• Sum of external forces acting on the system = 𝐹

3.15 The Linear Momentum Equation (LME) 𝜕 𝜕𝑡 (^) 𝑉

𝐴

• We call this equation the linear momentum equation (LME).
• We will limit our application of this equation to fixed, non-deforming control volumes.
• The external forces considered are body and surface forces that act on what is contained in the control volume.

3.15 The Linear Momentum Equation (LME)

• p 1 and p 2 are the gage pressures at the inlet and outlet, respectively.

3.15 The Linear Momentum Equation (LME)

• The resultant force R is given by: 𝑅 = 𝑅𝑥 2 + 𝑅𝑦 2
• The angle this force makes with the horizontal plane is: 𝜃 = 𝑡𝑎𝑛 − 1

3.15 The Linear Momentum Equation 3.15.1 Class Exercise

Water is flowing at a rate of 0.03154 m

3

/s through a horizontal

nozzle and discharges to the atmosphere at point (2). The nozzle is

attached at the upstream end at point (1) and friction forces are

considered negligible. The upstream inner diameter (ID) is 0.

m and the downstream ID is 0.0286 m. Calculate the resultant

force on the nozzle.

3.15 The Linear Momentum Equation 3.15.3 Class Exercise

Water is flowing at steady-state at 363 K and at a rate of 0.

m

3 /s through a 60˚ reducing bend (  2 = 60˚). The inlet pipe

diameter is 0.1016 m and the outlet 0.0762 m. The friction loss in

the pipe bend can be estimated as 𝑣 2

2

/ 5. Neglect gravity forces.

The exit pressure p 2 = 111.5 kN/m

2

gage. Calculate the resultant

force on the bend in Newtons.

Syllabus  Introduction to Fluid Mechanics and its Basic Concepts  Properties of Fluids  Pressure and Fluid Statics

• Mass, Momentum and Energy Conservation Equations
• Flow in Pipes
• Losses in Piping System
• Piping Network and Pump Selection

References (PFF260S)

• Cengel, Y.A. & Cimbala, J.M. 2013. Fluid Mechanics: fundamentals and applications. 3 rd ed. New York: McGraw-Hill.
• Perry, R.H., Green, D.W. & Maloney, J.O. (eds). 1998. Perry’s chemical engineer’s handbook. 7th^ ed. McGraw Hill: New York.
• Anderson, J.D. 1995. Computational fluid dynamics: the basics with applications. New York: McGraw-Hill.