Farhan Mohamed Ali (W2-1) Jigar Vora (W2-2) Sonali Kapoor (W2-3) Avni Jhunjhunwala (W2-4)
W2 Example 4 Answers
Transcript of 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