Fluids HW Practice Problem 13.1 1 of 9 Constants Let\'s begin with a simple calc

Question

 Fluids HW

Practice Problem 13.1

 1 of 9 

Constants

Let's begin with a simple calculation of the weight of air using density. Find the mass of air and its weight in a living room that has a 4.3m×6.3m floor and a ceiling 2.9 m high. What are the mass and weight of an equal volume of water?

SOLUTION

SET UP AND SOLVE Even for a problem like this, a simple sketch such as the one in helps to prevent mistakes. First we'll find the volume of the room; then we’ll use the density of air to find the mass of air it contains. The room's volume is

V=l×w×h=(4.3m)(6.3m)(2.9m)=78.561m3

Air has a density of =1.2kg/m3. The mass of the air in the room is

m=V=(1.2kg/m3)(78.561m3)=94.2732kg

The weight of the air is

w=mg=(94.2732kg)(9.8m/s2)=923.9N

The density of water is =1.0×103kg/m3. Thus, the mass of a volume of water that would fill the room is

m=V=(1000kg/m3)(78.561m3)=7.8561×104kg

The weight is

w=(7.8561×104kg)(9.8m/s2)=7.699×105N

REFLECT The weight of the air is about 208 lb . Does it surprise you that a roomful of air weighs this much? But the weight of the same volume of water is about 1.73×105lb , or 86.5 tons! This much weight would certainly collapse the floor of an ordinary house.

Part A - Practice Problem:

What volume of water would have a mass equal to the mass of air in the room?

Express your answer in liters to two significant figures.

Explanation / Answer

Mass of air= 94.2732 kg

Let the volume of water be V

Mass of water= VP where p is the density of water

Since the mass should be same

94.2732 = V*1000

V= 0.09427 m3

Since 1 cubic metres= 1000 litres

V= 94.2732 lites

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