Taking atmospheric pressure as 101,320 N/m², convert the following gauge pressures into absolute pressure (give your answer in kN/m² or kPa): (a) 400 kN/m², (b) 20 MN/m², (c) 5000 Pa and (d) 3000 psi.

Question

Accepted Answer

We know from above that absolute pressure is equal to gauge pressure plus atmospheric pressure, so the only real problem here is to ensure the correct conversion of units.

Atmospheric pressure = 101.32 kN/m².

a) 400 + 101.32 = 501.32 kN/m²

b) 20,000 + 101.32 = 20,101.32 kN/m² (note that MNm[latex]^{−2}[/latex] is the index way of writing MN/m²)

c) 5 + 101.32 = 106.32 kN/m² (remember that 1 Pa = 1 N/m²)

d) From Table 4.7,

Quantity	SI unit	Conversion factor→	Imperial/other recognized units
Acceleration	metre/second² (m/s²)	3.28084	feet/second² (ft/s²)
Angular measure	radian (rad)	57.296	degrees (°)
	radian/second (rad/s)	9.5493	revolutions per minute (rpm)
Area	metre² (m²)	10.7639	feet² (ft²)
	metre² (m²)	6.4516 × [latex]10^4[/latex]	inch² (in²)
Density	kilogram/metre³ (kg/m³)	0.062428	pound/foot³ (lb/ft³)
	kilogram/metre³ (kg/m³)	3.6127 × [latex]10^{-5}[/latex]	pound/inch³ (lb/in³)
	kilogram/metre³ (kg/m³)	0.010022	pound/gallon (UK)
Energy, work, heat	joule (J)	0.7376	foot pound-force (ft lbf)
	joule (J)	9.4783 × [latex]10^{-4}[/latex]	British thermal unit (btu)
	joule (J)	0.2388	calorie (cal)
Flow rate	m³ /s (Q)	35.315	ft³ /s
	m³ /s (Q)	13,200	gal/min (UK)
Force	Newton (N)	0.2248	pound-force (lbf)
	Newton (N)	7.233	poundal
	kilo-Newton	0.1004	ton-force (UK)
Heat transfer	watt (W)	3.412	btu/h
	watt (W)	0.8598	kcal/h
	watt/metre² kelvin (W/m² K)	0.1761	btu/h ft² °F
Illumination	lux (lx)	0.0929	foot candle
	lux (lx)	0.0929	lumen/foot² (lm/ft²)
	candela/metre² (cd/m²)	0.0929	candela/ft² (cd/ft²)
Length	metre (m)	1 × 1010	angstrom
	metre (m)	39.37008	inch (in)
	metre (m)	3.28084	feet (ft)
	metre (m)	1.09361	yard (yd)
	kilometre (km)	0.621371	mile
	kilometre (km)	0.54	nautical miles
Mass	kilogram (kg)	2.20462	pound (lb)
	kilogram (kg)	35.27392	ounce (oz)
	kilogram (kg)	35.27392	slug
	tonne (t)	0.984207	ton (UK)
	tonne (t)	1.10231	ton (US)
Moment, torque	Newton-metre (Nm)	0.73756	foot pound-force (ft lbf)
	Newton-metre (Nm)	8.8507	inch pound-force (in. lbf)
Moment of inertia (mass)	kilogram-metre squared (kgm²)	0.7376	slug-foot squared (slug ft²)
Second moment of area	millimeters to the fourth ([latex]mm^4[/latex])	2.4 × [latex]10^{-6}[/latex]	inch to the fourth (in[latex]^4[/latex])
Power	watt (W)	3.4121	British thermal unit/hour (btu/h)
	watt (W)	0.73756	foot pound-force/second (ft lbf/s)
	kilowatt (kW)	1.341	horsepower
	horsepower (hp)	550	foot pound-force/second (ft.lbf/s)
Pressure, stress	kilopascal (kPa)	0.009869	atmosphere (atm)
	kilopascal (kPa)	0.145	pound-force/inch² (psi)
	kilopascal (kPa)	0.01	bar
	kilopascal (kPa)	0.2953	inches of mercury
	pascal	1.0	Newton/metre² (N/m²)
	megapascal (MPa)	145.0	pound-force/inch² (psi)
Temperature	kelvin (K)	1.0	celsius (C)
	kelvin (K)	1.8	rankine (R)
	kelvin (K)	1.8	fahrenheit (F)
	kelvin (K)		°C + 273.15
	kelvin (K)		(°F + 459.67)/1.8
	celsius (°C)		(°F – 32)/1.8
Velocity	metre/second (m/s)	3.28084	feet/second (ft/s)
	metre/second (m/s)	196.85	feet/minute (ft/min)
	metre/second (m/s)	2.23694	miles/hour (mph)
	kilometre/hour (kph)	0.621371	miles/hour (mph)
	kilometre/hour (kph)	0.5400	knot (international)
Viscosity (kinematic)	square metre/second (m² /s)	1 × [latex]10^{6}[/latex]	centi-stoke
	square metre/second (m² /s)	1 × [latex]10^{4}[/latex]	stoke
	square metre/second (m² /s)	10.764	square feet/second (ft² /s)
Viscosity (dynamic)	pascal second (Pa s)	1000	centipoise (cP)
	centipoise (cP)	2.419	pound/feet hour (lb/ft h)
Volume	cubic metre (m³)	35.315	cubic feet (ft³)
	cubic metre (m³)	1.308	cubic yard (yd³)
	cubic metre (m³)	1000	litre (l)
	litre (l)	1.76	pint (pt) UK
	litre (l)	0.22	gallon (gal) UK

[latex]\frac{3000 \ psi }{0.145}[/latex] = 20,689.6 kN/m²

Question 4.46: Taking atmospheric pressure as 101,320 N/m², convert the fol...

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