Page 19 typically falls within Chapter 2, which is dedicated to the and their graphical solutions . Specifically, page 19 is where Parmakian transitions from deriving the theoretical celerity of a pressure wave to presenting the first complete graphical example of a valve closure problem.
University courses in hydraulic transients still use Parmakian because he forces students to understand the , not just software clicks. The derivation on page 19 of the wave speed equation is still exam material.
If you cannot locate the , modern resources have replicated his work:
Water hammer occurs when a fluid in motion is forced to stop or change direction suddenly. This is most commonly caused by the rapid closing of a valve or the sudden shutting down of a pump. Because water is incompressible (or nearly so), the momentum of the moving fluid creates a spike in pressure that travels as a wave through the piping system. water hammer analysis parmakian pdf 19
A third, more mundane possibility: "19" refers to a page number in a circulating in engineering forums (e.g., ResearchGate, Academia.edu, or a university repository). Many scanned copies from the 2010s have missing front matter; thus, the user is looking for the exact page where Parmakian solves a 10-inch pipe steel penstock example. In those scans, the example of valve closure with ( T_c = 2.5 ) seconds and ( L = 1500 ) ft begins at page 19.
In many prints of Water Hammer Analysis , falls within the foundational chapter entitled "Basic Equations for Rigid and Elastic Pipes." This page typically introduces the critical formula for celerity (wave speed) :
CFD and transient solvers are black boxes to many. Parmakian’s textbook examples (e.g., problem 3-2 on valve closure in a 1,200 m pipeline) provide that serve as a benchmark. If your software doesn’t match Parmakian’s page 19 example, you have a bug. Page 19 typically falls within Chapter 2, which
One of the most cited sections of Parmakian’s work is his detailed treatment of wave speed. The speed at which a pressure wave travels through a pipe depends heavily on the elasticity of the pipe wall and the bulk modulus of the liquid. Parmakian provides precise formulas and charts to calculate this variable, accounting for factors like:
To the practicing engineer: Find a legitimate copy, laminate page 19, and keep it in your field notebook. To the student: Understand Parmakian before you touch a software license. And to the historian: Recognize that in an age of AI and big data, a 1955 PDF page still stops water hammers more reliably than many modern apps.
: Simplifies analysis by assuming fluid is incompressible and pipe walls are rigid, suitable for slow transient events. The derivation on page 19 of the wave
$$ \Delta P = \rho \cdot a \cdot \Delta V $$
Ensure compliance with local copyright laws when downloading full-text technical manuals. If you need help analyzing a specific system, let me know: The pipe material and total length The fluid flow rate or velocity The valve closure time