158 Chapter 6 Fundamental Dimensions and Units
degree Rankine (°R), respectively, what is the appro-
priate unit for gas constant Rif the ideal gas law is to
be homogeneous in units?
6.41. For the fin equation described in Problem 6.25, if the
units of T, h, P, A, and xare expressed in degree
Rankine (°R), Btu /hft
2
°R, ft, ft
2
, and ft, respec-
tively, what is the appropriate unit for thermal con-
ductivity kif the fin equation is to be homogeneous in
unit? Show all steps of your work.
6.42. For Example 6.3 part (a), if the units of d, P, L, and A
are given in inches, lbf, inches, and in
2
, respectively,
what are the units for modulus of elasticity E?
6.43. For Example 6.3 part (b), if the units of k, A, T 1 T 2 ,
and Lare given in Btu /hft°F, ft
2
,°F, and ft, respec-
tively, what is the appropriate unit for heat transfer rate q?
6.44. For the drag coefficient relationship given in
Problem 6.24, if the units of Fd, V, A, and Cd, are
expressed in N, m/s, m
2
, and unitless, respectively,
what is the appropriate unit for?
6.45. For the cantilever beam relationship given in Problem 6.21,
if the units of y, w, E, x, and Lare expressed in inches,
lbf/in, lbf/in
2
, inches, and inches, respectively, what is the
appropriate unit for I?
6.46. The rotation of a rigid object is governed by the
following relationship: MI, where Msum
of the moments due to external forces (Nm), I
mass moment of inertia, and angular acceleration
of the object (rad /s
2
). What is the appropriate unit for
mass moment of inertia I?6.47. The value of viscosity of a fluid represents a measure of
how easily the given fluid can flow. The higher the vis-
cosity value is, the more resistance the fluid offers to
flow. For example, it would require less energy to trans-
port water in a pipe than it would to transport motor
oil or glycerin. The viscosity of many fluids is governedby Newton’s law of viscosity where is
shear stress (N/m
2
), is viscosity, and duis change in
flow speed ( m/s) over a height dy( m). What is the
appropriate unit for viscosity?6.48. The power output of a water turbine is given by P
gQh, where Pis power, is density of water (kg /m
3
),
gis acceleration due to gravity ( m/s
2
), Qis water flow
rate ( m
3
/s), and his the available water head ( m). What
is the appropriate unit for P?
6.49. The head loss due to flow of a fluid inside a pipe iscalculated from , where hLoss( m), fis
friction factor, Lis pipe length ( m), Dis pipe diameter
( m), Vis average flow velocity ( m/s), and gis the accel-
eration due to gravity ( m/s
2
). What is the appropriate
unit for friction factor f?6.50. For Problem 6.49, hLossis expressed in feet, Land Din
inches, Vin (ft /s), and gin (ft /s
2
). What is the appro-
priate unit for the friction factor f?hLossf
L
D
V
22 g
tm
du
dy
,
“Nothing is too wonderful to be true if it be consistent with the laws of nature.”
—Michael Faraday (1791–1867)Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀