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Textbook Question Chapter 3, Problem 3.1P

Perform the following estimations without using a calculator.

1. Estimate the mass of water (kg) in an Olympic-size swimming pool.
2. A drinking glass is being filled from a pitcher. Estimate die mass flow rate of the water (g/s).
3. Twelve male heavyweight boxers coincidentally get on the same elevator in Great Britain. Posted on the elevator wall is a sign that gives the maximum safe combined weight of the passengers, Wmax, in stones. (A stone is a unit of mass equal to 14 lbm. It is commonly used in England as a measure of body weight, which, like the numerical equivalence between the lbm and lbf, is only valid at or near sea level.) If you were one of the boxers, estimate the lowest value of Wniaxfor which you would feel comfortable remaining on the elevator.
4. The Trans-Alaska Pipeline has an outside diameter of 4 ft and extends 800 miles from the North Slope of Alaska to the northernmost ice-free port in Valdez, Alaska. How many barrels of oil arc required to fill the pipeline?
5. Estimate the volume of your body (cm3) in two different ways. (Show your work.)
6. A solid block is dropped into water and very slowly sinks to the bottom. Estimate its specific gravity.

Expert Solution Interpretation Introduction

(a)

Interpretation:

The mass of water (kg) in an Olympic-size pool should be estimated.

Concept introduction:

The density is the ratio of mass and volume given as:

ρ=mV

Here, m is mass and V is volume

2.5×106kg.

### Explanation of Solution

Let,

The size of a pool is 50m×25m×2m

The density of water is 1000kg/m3

Since, the formula for density is:

ρ=mV

Thus,

m=ρ×V

The mass of water is:

=50m×25m×2m×1000kg/m3=2.5×106kg

Expert Solution Interpretation Introduction

(b)

Interpretation:

The mass flow rate of the water (g/s) should be estimated.

Concept introduction:

An arithmetical multiplier which is used for converting a quantity expressed in one unit into another equivalent set of units is said to be conversion factor.

The relationship between US and SI units are,

1cm3=0.00105669qt1oz=0.03125qt

100g/s.

### Explanation of Solution

We can assume that the pitcher is a ‘large jug’.

In US standard system the volume of a drinking water glass is 8 oz and we can assume that the glass can be filled within 2 seconds using the pitcher.

The answer can be calculated as:

=(8oz2s)=4oz/sConvertunitstoSIsystem=(4oz/s)(1qt32oz)(106cm31056.68qt)(1gcm3)100g/s

Expert Solution Interpretation Introduction

(c)

Interpretation:

The lowest value of maximum weight (Wmax) for which you would feel comfortable remaining on the elevator should be estimated.

Concept introduction:

An arithmetical multiplier which is used for converting a quantity expressed in one unit into another equivalent set of units is said to be conversion factor. A stone is a unit of mass equal to 14 lbm.

220 stones.

### Explanation of Solution

A boxer who weight 220 lbm or above is considered as the boxer in heavy weight category.

The weight of a boxer can be considered as 220 lbm.

So calculate the minimum weight,

Wmax(12×220lbm14lbm)1stone220stones

Where Wmax is maximum weight.

Expert Solution Interpretation Introduction

(d)

Interpretation:

The number of barrels of oil required to fill the pipeline should be calculated.

Concept introduction:

The pipeline has an outside diameter of 4 ft and extends 800 miles.

The volume of a pipe (V) is given by,

V=πD2L4

Where, D = diameter of the pipe and L = length of the pipe

107barrels.

### Explanation of Solution

Let,

There are 42 gals in 1 barrel.

1 mile = 5880 ft

So the number of barrels in the pipe line can be calculated as,

NBarrels=πD2L4=(3.144)(4ft)2(800miles)(5880ft1mile)(7.48gal1ft3)(1barrel42gal)(3)(4)(5)(800)(5000)(7)(4)(4)(10)1×107barrels

Expert Solution Interpretation Introduction

(e)

Interpretation:

The volume of your body should be estimated in two different ways.

Concept introduction:

The density is the ratio of mass and volume given as:

ρ=mV

Here, m is mass and V is volume

### Explanation of Solution

Given Information:

The volume of the person is 6ft×1ft×0.5ft and the weight of the person is 150lbm.

Calculation:

Method 1:

Assume that the volume of the person can be considered as,

Height = 6 ft, width = 1 ft, thickness (distance between heal and toe) = 0.5 ft

Unit conversion,

1 ft3= 28 317 cm3

The volume of the person,

6ft×1ft×0.5ft(28,317cm31ft3)1×105cm3

Method 2:

Assume,

The weight of the person to be 150 lbm

The density of the person to be 62.4 lbm / ft3

Volume = mass / density

The volume of the person,

150lbm(1ft362.4lbm)28,317cm31ft3150×3×104601×105cm3

Expert Solution Interpretation Introduction

(f)

Interpretation:

The specific gravity of a solid block in water should be calculated.

Concept introduction:

The specific gravity of a body with respect to water is calculated by taking ratio of density of that body to the density of water. It is also related to molar mass as follows:

S=ρAρB=MAMB

Here, ρA is density of body A and ρB is density of water.

1.05

### Explanation of Solution

Since, the solid block sinks into the water very slowly, the density of block should be close to the density of water. So, assume density of the block to be 1050 kg / m3.

The Specific gravity is calculated as follows:

S=ρAρB

Putting the values,

S=1050kg/m31000kg/m3=1.05

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