Units Conversion Part 1. Express 65 mph in (a) ft/s, and (b) m/s. Part 2. The density of 35 °API crude oil is 53.1 lbm/ft^3 at 68 °F, and its viscosity is 32.8 lbm/ft hr. What are its density, viscosity, and kinematic viscosity in SI units?

Question

Units Conversion

Part 1. Express [latex]65 \mathrm{mph}[/latex] in (a) [latex]\mathrm{ft} / \mathrm{s}[/latex], and (b) [latex]\mathrm{m} / \mathrm{s}[/latex].

Part 2. The density of [latex]35^{\circ}[/latex] API crude oil is [latex]53.1 \mathrm{lb}_{\mathrm{m}} / \mathrm{ft}^{3}[/latex] at [latex]68^{\circ} \mathrm{F}[/latex], and its viscosity is [latex]32.8 \mathrm{lb}_{\mathrm{m}} / \mathrm{ft} \mathrm{hr}[/latex]. What are its density, viscosity, and kinematic viscosity in SI units?

Accepted Answer

Part 1. The solution is obtained by employing conversion factors taken from Table 1.11:

Table 1.11 Commonly Used Conversion Factors
Area	1 [latex]mile^{2} [/latex]	=	640 acres
	1 acre	=	0.4047 ha
Energy	1 BTU	=	1,055 J
	1 cal	=	4.184 J
	1 J	=	0.7376 ft [latex]lb_{f}[/latex]
	1 erg	=	1 dyne cm
Force	1 [latex]lb_{f}[/latex]	=	4.448 N
	1 N	=	0.2248 [latex]lb_{f}[/latex]
Length	1 ft	=	0.3048 m
	1 m	=	3.281 ft
	1 mile	=	5,280 ft
Mass	1 [latex]lb_{m}[/latex]	=	0.4536 kg
	1 kg	=	2.205 [latex]lb_{m}[/latex]
Power	1 HP	=	550 ft[latex]lb_{f}[/latex]/s
	1 kW	=	737.6 ft[latex]lb_{f}[/latex]/s
Pressure	1 atm	=	14.696[latex]lb_{f} /in^{2} [/latex]
	1 atm	=	1.0133 bar
	1 atm	=	1.0133 × [latex]10^{5}[/latex] Pa
Time	1 day	=	24 hr
	1 hr	=	60 min
	1 min	=	60 s
Viscosity	1 cP	=	2.419 [latex]lb_{m}[/latex]/ft hr
	1 cP	=	0.001 kg/m s
	1 cP	=	0.000672 [latex]lb_{m}[/latex]/ft s
	1 [latex]lb_{f} s /ft^{2} [/latex]	=	4.788 × [latex]10^{4}[/latex] cP
Volume	1 [latex]ft^{3} [/latex]	=	7.481 U.S. gal
	1 U.S. gal	=	3.785 l
	1 [latex]m^{3} [/latex]	=	264.2 U.S. gal

(a) [latex]65 \frac{\mathrm{mile}}{\mathrm{hr}} imes \frac{1}{3,600} \frac{\mathrm{hr}}{\mathrm{s}} imes 5,280 \frac{\mathrm{ft}}{\mathrm{mile}}=95.33 \frac{\mathrm{ft}}{\mathrm{s}}[/latex].

(b) [latex]95.33 \frac{\mathrm{ft}}{\mathrm{s}} imes 0.3048 \frac{\mathrm{m}}{\mathrm{ft}}=29.06 \frac{\mathrm{m}}{\mathrm{s}}[/latex].

Part 2.

[latex]\begin{aligned} ho &=53.1 \frac{\mathrm{lb}_{\mathrm{m}}}{\mathrm{ft}^{3}} imes 0.4536 \frac{\mathrm{kg}}{\mathrm{lb}_{\mathrm{m}}} imes \frac{1}{0.3048^{3}} \frac{\mathrm{ft}^{3}}{\mathrm{~m}^{3}}=851 \frac{\mathrm{kg}}{\mathrm{m}^{3}}. \ \mu &=32.8 \frac{\mathrm{lb}_{\mathrm{m}}}{\mathrm{ft} \mathrm{hr}} imes \frac{1}{2.419} \frac{ ext { centipoise }}{\mathrm{lb}_{\mathrm{m}} / \mathrm{ft} \mathrm{hr}} imes 0.01 \frac{ ext { poise }}{ ext { centipoise }}=0.136 ext { poise. }\end{aligned}[/latex]

Or, converting to SI units, noting that [latex]\mathrm{P}[/latex] is the symbol for poise, and evaluating [latex] u[/latex] :

[latex]\begin{array}{l}\mu=0.136 \mathrm{P} imes 0.1 \frac{\mathrm{kg} / \mathrm{m} \mathrm{s}}{\mathrm{P}}=0.0136 \frac{\mathrm{kg}}{\mathrm{m} \mathrm{s}}. \ u=\frac{\mu}{ ho}=\frac{0.0136 \mathrm{~kg} / \mathrm{m} \mathrm{s}}{851 \mathrm{~kg} / \mathrm{m}^{3}}=1.60 imes 10^{-5} \frac{\mathrm{m}^{2}}{\mathrm{~s}} \quad(=0.160 \mathrm{St}).\end{array}[/latex]

Question 1.1: Units Conversion Part 1. Express 65 mph in (a) ft/s, and (b)...

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