daft engineer

engineering my way through a cup of coffee

Hoop stress and wall thickness in storage tanks

In my ongoing quest to reinvent all the equations in all the engineering codes, I found myself idly wondering why the equations of shell thickness in API 650 are the way they are. You would think that the governing stress in a storage tank is the hoop stress, and the …

tags: API 650, hoop stress, python,

Storage tank venting and API 2000

A previous post talked about venting through a gooseneck, where I just assumed the amount of venting had already been figured out. This time I want to go into more details of the API-2000 method for venting, the assumptions, and the models.

(The following deals with the 2014 edition of …

tags: API 2000, venting,

Sizing a goose neck vent

This is one of those random things that came up, through work, where I was surprised to find a relative void of info on the internet: sizing a gooseneck for an aboveground storage tank.

Venting for aboveground storage tanks is dealt with in standards such as API 2000, which gives …

tags: API 2000, venting, compressible flow, fanno flow, pipe flow,

Two dimensional turbulent jet -- part 2

Continuing on with the analysis of turbulent flow in a jet issuing out of a small slit running along the x-y axis with length (in the y-direction) W and basically no width. The flow issues forth in the positive z direction into a semi-infinite reservoir of stationary fluid (same fluid …

tags: fluid dynamics, jet,

Two dimensional turbulent jet -- part 1

Moving into turbulent flow now, I'm going to look at a jet issuing out of a small slit running along the x-y axis with length (in the y-direction) W and basically no width. The flow issues forth in the positive z direction into a semi-infinite reservoir of stationary fluid (same …

tags: fluid dynamics, jet,

Visualizing transient laminar pipeflow

transient pipe flow

In a previous post I derived some equations for the velocity distribution as a function of time in transient pipe flow. Here it is visualized by Sage.

The Sage code is as follows

import mpmath as mp
xi, tau = var('xi tau')

def phi(xi,tau,n):
    sum = 0
    for …

tags: fluid dynamics, pipe flow,

Startup of laminar pipe flow

I've spent a fair bit of time examining various kinds of pipe flow, but so far only at steady state. This time I take a kick at the transient flow cat, looking at start-up of laminar pipe flow (Transport Phenomena 4D.2)

Suppose the same old cylindrical coordinates, assuming incompressible …

tags: fluid dynamics, pipe flow,

Flow through a porous medium, with pipes!

Flow in and around pipes is old hat at this point, so to keep things fresh what about flow through porous medium, into a pipe? (Transport Phenomena 4C.4)

porous tube

Suppose fluid is coming in through the walls of a pipe, say a ceramic tube with a pressure at the outside …

tags: pipe flow, fluid dynamics,

The pressure field around a bubble

Previously, I figured out the velocity field for creeping flow around a bubble, and made a nice graphic to go with. This time I solved through for the pressure field, and this is what it looks like (along the plane y=0, gauge pressure, all other constants 1) pressure in flow passed a bubble

The derivation …

tags: fluid dynamics, creeping flow, gas,

Creeping flow around a bubble

When fluid flows around a gas bubble, circulation within the bubble dissipates energy away from the interface and the interfacial shear stress is reduced. In this problem (4B.3 Transport Phenomena) I look at what happens when that shear stress is negligible.

creeping flow around a bubble

Flow is coming up along the positive z-axis …

tags: fluid dynamics, creeping flow, gas,

time and space dependent velocities: the case of suddenly applied wall stress

Previous examples in fluid mechanics assumed steady state. This time lets try something else and imagine a simple non-steady state scenario. Imagine a semi-infinite fluid bounded by a wall at y=0, what happens if the shear stress at the wall undergoes a step-change, at time t=0, to some …

tags: fluid dynamics,

From Newton's Second Law to the Equations of Change for a fluid

Most often when you see the derivation for the general form of the equations of change for fluid dynamics it is done by considering some differential element. What follows is a way of arriving at the same result by considering Newton's second law for an arbitrary volume of fluid moving …

tags: fluid dynamics,

Using the Bernoulli equation to derive Toricelli's equation

Bernoulli's equation for fluid flow along a streamline is a really useful go-to equation for explaining various fluid mechanics phenomena, and if you extend it by taking into account friction you end up with the engineering Bernoulli equation or a mechanical energy balance, which is practically the default starting point …

tags: fluid dynamics,

Pipe strength and the mysterious "Y"

Recently, at work, there was some work where someone needed to break out ASME B31.3 and figure out the allowable pressure for a given length of pipe -- back calculating from what was there to what was "OK".

tags: ASME B313, hoop stress,

Flow constrained by concentric spheres

The last few flow problems I toyed with used a simple momentum balance as the starting point, time to move on to other ways to solve flow problems such as the continuity equation and the equations of motion for the fluid (e.g. the Navier-Stokes equations ).

Today I'm going to …

tags: fluid dynamics,

Not no-slip -- low density gas flow

Continuing on with tube flow, what happens when the fluid moving through the tube is low density and thus the no-slip boundary condition breaks down? (from 2B.9 Transport Phenomena)

I want the mass flowrate for a low density gas moving through a tube in slip flow.

First off we …

tags: fluid dynamics, pipe flow, compressible flow,

Liquid in and on pipes

One of the nice things about setting up the math for simple fluid flow problems is that you can recycle the initial bits for various other uses. If you set up a balance based on a particular geometry of a differential volume then a wide variety of possible flow cases …

tags: fluid dynamics, pipe flow,

The ideal gas law from Maxwell's velocity distribution

Recently I've been playing around with finding the relations between the microscopic particulars of an ideal gas and the macroscopic observables we all know and love -- in particular the relation between temperature and the average kinetic energy (velocity) of the particles in the gas. We can take the idea further …

tags: kinetic theory, gas,

Mathematical interlude

Last time I poked around with calculating the mean velocity of the particles in a gas from the Maxwell distribution of velocities. While doing so I bashed my way through some integrals that, on reflection, are much easier when I remembered that they are in the back of some of …

Average velocity of the molecules in a gas

In this problem I aim to show that the expression for the average velocity of particles in a gas can be derived from the Maxwell velocity distribution (problem 1C.1(a) Transport Phenomena).

In the kinetic molecular theory of gases, velocities are randomly distributed and have an average magnitude given …

tags: kinetic theory, gases,

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