w2 example 4 answers

4a Using the other units given in the question, deduce the

units of wind stress. What else is this unit known as?

What is it a measure of?

4a Note: Brackets around 𝜏 represent its units.

• Replace the values in the first equation for their units:

4a Note: Brackets around 𝜏 represent its units.

• Replace the values in the first equation for their units:

(τ) = kgm−3. ms−1. ms−1

4a Note: Brackets around 𝜏 represent its units.

• Replace the values in the first equation for their units:

(τ) = kgm−3. ms−1. ms−1

• Group the same units together and simplify:

4a Note: Brackets around 𝜏 represent its units.

• Replace the values in the first equation for their units:

(τ) = kgm−3. ms−1. ms−1

• Group the same units together and simplify:

(τ) = kg (m−3. m1. m1)(s−1. s−1)

4a Note: Brackets around 𝜏 represent its units.

• Replace the values in the first equation for their units:

(τ) = kgm−3. ms−1. ms−1

• Group the same units together and simplify:

(τ) = kg (m−3. m1. m1)(s−1. s−1)

(τ) = 𝐤𝐠𝐦−𝟏𝐬−𝟐

4a Note: Brackets around 𝜏 represent its units.

• Replace the values in the first equation for their units:

(τ) = kgm−3. ms−1. ms−1

• Group the same units together and simplify:

(τ) = kg (m−3. m1. m1)(s−1. s−1)

(τ) = 𝐤𝐠𝐦−𝟏𝐬−𝟐

This unit is also known as a Pascal, Pa. It is a unit of pressure.

4b What wind speed would produce a drag coefficient of 1.05

x 10-3?

4b • Substitute the values you know into the second equation:

4b • Substitute the values you know into the second equation:

1.05 x 10−3 = 0.53 + 0.064U x 10−3

4b • Substitute the values you know into the second equation:

1.05 x 10−3 = 0.53 + 0.064U x 10−3

• Cancel out 10-3:

4b • Substitute the values you know into the second equation:

1.05 x 10−3 = 0.53 + 0.064U x 10−3

• Cancel out 10-3:

1.05 = 0.53 + 0.064U

4b • Substitute the values you know into the second equation:

1.05 x 10−3 = 0.53 + 0.064U x 10−3

• Cancel out 10-3:

1.05 = 0.53 + 0.064U

• Rearrange for U:

4b • Substitute the values you know into the second equation:

1.05 x 10−3 = 0.53 + 0.064U x 10−3

• Cancel out 10-3:

1.05 = 0.53 + 0.064U

• Rearrange for U:

1.05 − 0.53 = 0.064U

4b • Substitute the values you know into the second equation:

1.05 x 10−3 = 0.53 + 0.064U x 10−3

• Cancel out 10-3:

1.05 = 0.53 + 0.064U

• Rearrange for U:

1.05 − 0.53 = 0.064U

U =1.05 − 0.53

0.064= 𝟖. 𝟏𝟐𝟓𝐦𝐬−𝟏

4c Using only the first equation for wind stress, calculate the

wind speed needed to produce a wind stress of 4.9 x 10-2

Pa. Assume the density of air is 1.225 kgm3 and the drag

coefficient is 9.46 x 10-4.

4c • Rearrange the first equation for U:

4c • Rearrange the first equation for U:

ρACDU2 = τ

4c • Rearrange the first equation for U:

ρACDU2 = τ

U2 =τ

ρACD

4c • Rearrange the first equation for U:

ρACDU2 = τ

U2 =τ

ρACD

U =τ

ρACD

4c • Rearrange the first equation for U:

ρACDU2 = τ

U2 =τ

ρACD

U =τ

ρACD

• Substitute in the values you know:

4c • Rearrange the first equation for U:

ρACDU2 = τ

U2 =τ

ρACD

U =τ

ρACD

• Substitute in the values you know:

4.9 x 10−2

1.225 x 9.46 x 10−4= 𝟔. 𝟓𝟎𝐦𝐬−𝟏