information.The hard problems often require obscure information. Works with nature,not against it.Do not enter a problem with preconceived notions about how it must be solved.Nature will often guide you through the solution if you are attentive to its whispers. Keeps an engineering "toolbox."An engineering "toolbox"is filled with simple qualitative relationships needed by the qualitative model in the subconscious.These simple qualitative relationships may be the distilled wisdom from quantitative engineering analysis.The following sections describe a few"tools."As you progress through your career,you will need a large toolbox to hold all the tools you acquire from your experience. 1.12.1 Cube-Square Law An example of information an engineer may store in her toolbox is the cube-square law.The cube-square law says that as an object gets smaller,its volume decreases much faster than its area.Therefore,the surface-area-to-volume ratio increases with smaller objects. To illustrate this law,imagine our object is a sphere(Figure 1.8).This surface area a is A=4π2 (1-2) And the volume V is 4 V=-πr (1-3) 3 The surface-area-to-volume ratio is A4πr23 ”三 (1-4) D4πr3r This equation says that the area-to volume ratio increases as the radius decreases. The cube-square law is one of the most overcharging laws in nature,as shown by the following examples: Example 1.1 Imagine you work in a cannonball factory that casts cannonballs from molten metal and cools them in air.From the cube-square law,you know that smaller cannonballs will cool down faster than the large cannonballs,because the rate of heat loss is affected by the surface area but the total amount of heat loss is determined by the cannonball volume. Example 1.2 Imagine that you must select the most energy-efficient method to fly 500 passengers from New York to Paris.You could charter five 100-passenger planes or one 500-passenger plane.Fuel is primarily required to overcome air drag,which is dictated by the plane surface area.Passenger capacity is determined by the plane volume.To improve fuel economy,you want a small surface area relative to the volume,so one large plane is better than five smaller planes. Example 1.3 You want to store 50,000 gallons of diesel fuel.You are contemplating purchasing one 50,000 gallon tank or five 10,000 gallon tanks.Tank vendors charge for the metal,not the air in the tank;therefore,tank cost is mostly determined by the surface area.information. The hard problems often require obscure information. · Works with nature, not against it. Do not enter a problem with preconceived notions about how it must be solved. Nature will often guide you through the solution if you are attentive to its whispers. · Keeps an engineering “toolbox.” An engineering “toolbox” is filled with simple qualitative relationships needed by the qualitative model in the subconscious. These simple qualitative relationships may be the distilled wisdom from quantitative engineering analysis. The following sections describe a few “tools.” As you progress through your career, you will need a large toolbox to hold all the tools you acquire from your experience. 1.12.1 Cube-Square Law An example of information an engineer may store in her toolbox is the cube-square law. The cube-square law says that as an object gets smaller, its volume decreases much faster than its area. Therefore, the surface-area-to –volume ratio increases with smaller objects. To illustrate this law, imagine our object is a sphere (Figure 1.8). This surface area A is 2 A  4 r (1-2) And the volume V is 4 3 3 V   r (1-3) The surface-area-to –volume ratio is 2 3 4 3 4 3 A r V r r     (1-4) This equation says that the area-to volume ratio increases as the radius decreases. The cube-square law is one of the most overcharging laws in nature, as shown by the following examples: Example 1.1 Imagine you work in a cannonball factory that casts cannonballs from molten metal and cools them in air. From the cube-square law, you know that smaller cannonballs will cool down faster than the large cannonballs, because the rate of heat loss is affected by the surface area but the total amount of heat loss is determined by the cannonball volume. Example 1.2 Imagine that you must select the most energy-efficient method to fly 500 passengers from New York to Paris. You could charter five 100-passenger planes or one 500-passenger plane. Fuel is primarily required to overcome air drag, which is dictated by the plane surface area. Passenger capacity is determined by the plane volume. To improve fuel economy, you want a small surface area relative to the volume, so one large plane is better than five smaller planes. Example 1.3 You want to store 50,000 gallons of diesel fuel. You are contemplating purchasing one 50,000 gallon tank or five 10,000 gallon tanks. Tank vendors charge for the metal, not the air in the tank; therefore, tank cost is mostly determined by the surface area