434 Measurement and Data Analysis for Engineering and Science
7. The Reynolds number, Re, is a dimensionless number used in fluid me-
chanics and is defined as Re = ρV D/µ, where ρ is the fluid density, µ
the fluid absolute viscosity, V the fluid velocity, and D the characteristic
length dimension of the body immersed in the moving fluid. Because this
number has no units, it should be independent of the system of units
chosen for ρ, µ, V , and D. In the International system of units, ρ = 1.16
kg/m
3
, µ = 1.85 × 10
−5
N·s/m
2
, V = 5.0 m/s, and D = 0.254 m. Using
this information, compute (a) values for ρ, µ, V , and D in the English
Engineering system, (b) Re based on the International System, and (c)
Re based on the English Engineering system.
8. The power coefficient, C
P
, for a propeller is a nondimensional number
that is defined as C
P
= P/(ρn
3
D
5
), where P is the power input to
the propeller, ρ the density of the fluid (usually air), n the propeller’s
revolutions per second, and D the propeller diameter. For ρ = 0.002 11
slug/ft
3
, n = 2400 rpm, D = 6.17 ft, and P = 139 hp, (a) express these
four values in SI units and (b) compute C
P
based on the SI units.
9. The advance ratio J for a propeller is defined as J = V/(nD), where
V is the velocity, n the propeller’s revolutions per second, and D the
propeller diameter. For V = 198 ft/s, n = 2400 rpm, and D = 6.17 ft,
(a) show that J is a nondimensional number by “balancing” the units
and (b) compute the value of J.
10. An engineering student measures an ambient lab pressure and temper-
ature of 405.35 in. H
2
O and 70.5
◦
F, respectively, and a wind tunnel
dynamic pressure (using a pitot-static tube) of 1.056 kN/m
2
. Assume
that R
air
= 287.04 J/(kg · K). Determine with the correct number of
significant figures (a) the room density using the perfect gas law in SI
units (state the units with the answer) and (b) the wind tunnel velocity
using Bernoulli’s equation in units of ft/s. Bernoulli’s equation states
that for irrotational, incompressible flow the dynamic pressure equals
one-half the product of the density times the square of the velocity.
11. An engineer using a barometer measures the laboratory temperature
and pressure to be 70.0
◦
F and 29.92 in. Hg, respectively. He then con-
ducts a wind tunnel experiment using a pitot-static tube and an inclined
manometer to determine the wind tunnel velocity through Bernoulli’s
equation. He measures a pressure difference of 3.22 in. H
2
O. Determine
the tunnel velocity and express it with the correct number of significant
figures in units of m/s.
12. A capacitor consists of two round plates, each of radius r = 5 cm. The
gap between the plates is d = 5 mm. Determine the maximum charge
q
max
of the capacitor in coulombs if the breakdown potential of the air
is U
max
= 10 kV. Find the capacitor energy in both the International
(SI) and the English Engineering (EE) systems.