Level curves for barometric pressure (in millibars) are shown for 6:00 AM on November 10, 1998. A deep low with pressure 972 mb is moving over northeast Iowa. The distance along the red line from K (Kearney, Nebraska) to S (Sioux City, Iowa) is 300 km. Estimate the value of the directional derivative of the pressure function at Kearney in the direction of Sioux City.

Question

14-09-2020
Mathematics

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Level curves for barometric pressure (in millibars) are shown for 6:00 AM on November 10, 1998. A deep low with pressure 972 mb is moving over northeast Iowa. The distance along the red line from K (Kearney, Nebraska) to S (Sioux City, Iowa) is 300 km. Estimate the value of the directional derivative of the pressure function at Kearney in the direction of Sioux City.

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nuhulawal20 nuhulawal20 · Answer 1 · 2020-09-19T11:19:41+02:00

Answer: the value of the directional derivative of the pressure function at Kearney in the direction of Sioux City is - 0.09 mb/km

Step-by-step explanation:

lets make an assumption that P is the pressure of the function

Now to estimate the value of the directional derivative of the pressure function at Kearney in the direction of Sioux City wil be DuP

The initial point of the line joining the point of kearney and sioux lays on the level curve which represent 1000mb of pressure

and the terminal point of the line joining the point of kearney and sioux lays on the level curve which represent 972 mb of pressure

so let our X1 = 1000 mb

X2 = 972 mb

the given distance between kearney and sioux d = 300 km

so the directional derivative DuP at Kearney in the direction of Sioux City is approximated by finding the average rate change of the pressure between the points

so DuP = (X2 - X1) / d

= (972 - 1000) / 300

= -28 / 300

= - 0.09 mb/km

Therefore the value of the directional derivative of the pressure function at Kearney in the direction of Sioux City is - 0.09 mb/km

MrRoyal MrRoyal · Answer 2 · 2021-10-24T13:18:34+02:00

Pressure is a measure of unit force acting on an area.

The estimated value of the directional derivative of the pressure function is -0.093mb/km

The given parameters from the complete question are:

[tex]\mathbf{P_1 = 972mb}[/tex]

[tex]\mathbf{P_2 = 1000mb}[/tex]

[tex]\mathbf{d = 300km}[/tex]

So, the value of the directional derivative of the pressure function is:

[tex]\mathbf{D\mu P = \frac{P_1 - P_2}{d}}[/tex]

This gives

[tex]\mathbf{D\mu P = \frac{972 - 1000}{300}}[/tex]

[tex]\mathbf{D\mu P = \frac{-28}{300}}[/tex]

[tex]\mathbf{D\mu P = -0.093}[/tex]

Hence, the estimated value of the directional derivative of the pressure function is -0.093mb/km