BE 350
Transport Processes
in Living Systems
3/17/2014
Viscous flow in pipes
Pipe flow
Pipe
flow
Open
channel
flow
Laminar & turbulent flow in a pipe
= density of fluid
= viscosity of fluid
U = characteristic velocity
L = characteristic length
Osborne R

Last quiz. BE350, 4124:9014 Name:
Question 1:
A vertical concentric annulus, with outer
radius 1'0 and inner radius 13-, is lowered into
ﬂuid of surface tension 0 and contact angle
6. Derive an expression for the capillary rise
11 in the annular gap. Assu

HW#1: fluid fundamentals - part 1
1/17/2014
1. A fluid is defined as a substance that deforms continuously under the action of (
of any magnitude.
) stress
2. Sand and other granular materials such as sugar definitely flow. That is, you can pour them
from

HW#8: Pipe
P
flow
Distributted: 3/14/201
14
Due: 3/20
0/2014
1. For a steady unifo
form flow off an incompreessible liquiid that enterss a pipe, whiich of the
follw
wing is true fo
or the entran
nce region.
(a) The
T average velocity
v
is a function of di

HW#2: fluid
f
fundam
mentals (part 2) & fluid
d statics (paart 1)
1/24/2014
1. For a parallel plaate arrangement of the ty
ype shown beelow in the ddiagram, it iss found that
when
n the distancee between pllates is 2 mm
m, a shearingg stress of 1550 Pa de

HW#6, BE350, Spring 2014: Energy and beginning of chapter 6, due 2/26/2014
Question #1 (5.115):!
The hydroelectric turbine at the right passes is at the
bottom of a lake of height H (50m). The exit velocity is
V2 (6 m/s) through an pipe of diameter D (1m)

Homework for diffusion, BE350, 4/12/2013
1. Lets say you photobleach (in 1D) a region between -L to L. What are the boundary conditions
for fluorescence recovery after photobleaching at -L, L? Sketch what the fluorescence in this
region will look like ove

HW#6, BE350, Spring 2014: Chapter 6, due 3/5/2014
Question #1 (6.88):!
Two fixed horizontal parallel plates are separates by a distance h. A fluid with viscosity
flows between the plates with a mean velocity V. The flow is laminar. Determine the
pressure

HW#1: fluid fundamentals - part 1
1/17/2014
1. A ﬂuid is deﬁned as a substance that deforms continuously under the action of ( ) stress
of any magnitude.
Shear (other acceptable answers: shearing, tangential)
2. Sand and other granular materials such as s

HW#2: fluid fundamentals (part 2) & fluid statics (part 1)
1/24/2014
1. For a parallel plate arrangement of the type shown below in the diagram, it is found that
when the distance between plates is 2 mm. a shearing stress of 150 Pa develops at the upper
p

HW#2: fluid fundamentals (part 2) & fluid statics (part 1)
1/24/2014
1. For a parallel plate arrangement of the type shown below in the diagram, it is found that
when the distance between plates is 2 mm. a shearing stress of 150 Pa develops at the upper
p

BE350 Midterm 2, 4/4/2014 Name:
Question 1. [10 pts: 2 pts each + 2 for getting all 4 right) The four devices shown below rest on
frictionless wheels, are restricted to move in the x direction only, and are initially held stationary.
The pressure at the i

Quiz #5: pipe flow
3/21/2014
I. For a very rough pipe wall, the friction factor is constant at high Reynolds numbers. The
pressure drop over the length of the pipe is A p;. If the diameter of the pipe is halved, what is
the relationship between the new pr

kfrui +9“;-
J_‘_._~_‘_—.
038 = ‘9 i 411;" gig-‘12,)
?.
- x i, «1:2 P!) =” g
- an mygg; ‘ = '- .
vsv mm. =v W5"
2 v1 j”,_f_‘+
' 1 Fl 0 2 b 6.‘ ‘3’ An incompressible viscous ﬂuid is placed
= between two large paraﬁcl ‘piatcs m shOWﬁ in Fig. 1
TM.

HW ﬁt? Solull'lsm
Question #1 (6.88):
Two ﬁxed horizontal parallel plates ate separates by a distance h. A fluid with viscosity
p flows between the plates with a mean velocity V. The flow is taminar. Determine the
pressure drop per unit length in the di

HW#8: Pipe ﬂow
Distributed: 3/14/2014
Due: 3/20/2014
1. For a steady uniform ﬂow of an incompressible liquid that enters a pipe, which of the
follwing is true for the entrance region.
(a) The average velocity is a function of distance from the entrance.
h

BE350 Quiz, 2/28/2014
1. Water flows through the valve below
at a rate Q. The pressure upstream is
p1 and the pressure downstream is p2.
The inner diameters are D1 and D2.
a. Ignoring the effects of gravity,
determine the loss in available
energy across t

A set of open capillary tubes with varying
diameters is inserted into water as shown at
right. Which of the following correctly
shows the equilibrium water levels in the
tubes?
(a)
(b)
(c)
(d)
2

x ~
BE350 Quiz, 312812014 Name:
Question 1: Suppose you have constant heat generation qg (qg > 0) in a biock from x =
-L1 to +L2. The heat conductance is k. Suppose further that the temperature distribution
is given by T(x) : a + bx2.
a) Draw a sketch of

BE350 Midterm 1 (Spring 2014) Name:
1. For low-speed steady flow of blood through a capillary vessel shown below, the velocity
along the blood vessel it varies with radius and takes the form
, where p is the fluid viscosity and Ap is the pressure drop f

Under the right conditions, it is possible to have metal objects float on water due to surface
tension. Consider placing a needle with diameter D, length L, and specific weight on the
surface of water with surface tension . What is the maximum diameter of

HW#3: fluid
f
statics (part 2)
Distributted: 1/31/201
14
Due: 2/5/2014
1. In thee diagram on
n the right, pressure
p
gagee A reads
1.5 kP
Pa (gage preessure). Thee fluids are at
a 20 C.
Deterrmine the eleevation z (in
n m) of the liquid levels
in thee ope

Homework 1 for Heat Transfer
Question 1: A hot water pipe with outside radius r1 has a temperature T1 . A thick
insulation applied to reduce the heat loss has an outer radius r2 and temperature
T2 . On T , r coordinates, sketch the temperature distributio

HW#2: fluid
f
fundam
mentals (part 2) & fluid
d statics (paart 1)
1/24/2014
1. For a parallel plaate arrangement of the ty
ype shown beelow in the ddiagram, it iss found that
when
n the distancee between pllates is 2 mm
m, a shearingg stress of 1550 Pa de

HW#4: Bernoulli
B
Distributted: 2/7/2014
4
Due: 2/12
2/2014
1. Water flows with
hout friction vertically do
ownward thrrough a pipe and enters a section whhere
the crross sectionaal area is larg
ger. The vellocity profilee is uniform at sections 1 and 2.

Sole
_——-—_
HW#5, BE350, Spring 2014: Material Derivative and Reynold’s transport, due 2/19/2014
Stagnation point, 5 = 0
Question #1 (4.35):
A fluid particle depicted to the right flows along
a stagnation streamline towards the stagnation
point. The parti