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Pressure gradient has the same dimensions as that of
- a)velocity gradient
- b)potential gradient
- c)energy gradient
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
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Pressure gradient has the same dimensions as that ofa)velocity gradien...
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Pressure gradient has the same dimensions as that ofa)velocity gradien...
Explanation:
Pressure gradient, velocity gradient, potential gradient, and energy gradient are all related to different physical quantities. Let's understand each of them in detail:
1. Pressure gradient: The pressure gradient is the rate of change of pressure with respect to distance. It is denoted by ∇P and has the unit of Pascal/meter. It is a measure of the change in pressure across a distance.
2. Velocity gradient: The velocity gradient is the rate of change of velocity with respect to distance. It is denoted by ∇v and has the unit of meter/second/meter. It is a measure of the change in velocity across a distance.
3. Potential gradient: The potential gradient is the rate of change of potential with respect to distance. It is denoted by ∇φ and has the unit of volt/meter. It is a measure of the change in potential across a distance.
4. Energy gradient: The energy gradient is the rate of change of energy with respect to distance. It is denoted by ∇E and has the unit of joule/meter. It is a measure of the change in energy across a distance.
Now, let's compare the dimensions of each of these gradients:
1. Pressure gradient: Pascal/meter
2. Velocity gradient: meter/second/meter
3. Potential gradient: volt/meter
4. Energy gradient: joule/meter
As we can see, each of these gradients has a different unit of measurement, which means that they are related to different physical quantities. Therefore, the correct answer to this question is option 'D' - none of these.
Pressure gradient, velocity gradient, potential gradient, and energy gradient are all related to different physical quantities. Let's understand each of them in detail:
1. Pressure gradient: The pressure gradient is the rate of change of pressure with respect to distance. It is denoted by ∇P and has the unit of Pascal/meter. It is a measure of the change in pressure across a distance.
2. Velocity gradient: The velocity gradient is the rate of change of velocity with respect to distance. It is denoted by ∇v and has the unit of meter/second/meter. It is a measure of the change in velocity across a distance.
3. Potential gradient: The potential gradient is the rate of change of potential with respect to distance. It is denoted by ∇φ and has the unit of volt/meter. It is a measure of the change in potential across a distance.
4. Energy gradient: The energy gradient is the rate of change of energy with respect to distance. It is denoted by ∇E and has the unit of joule/meter. It is a measure of the change in energy across a distance.
Now, let's compare the dimensions of each of these gradients:
1. Pressure gradient: Pascal/meter
2. Velocity gradient: meter/second/meter
3. Potential gradient: volt/meter
4. Energy gradient: joule/meter
As we can see, each of these gradients has a different unit of measurement, which means that they are related to different physical quantities. Therefore, the correct answer to this question is option 'D' - none of these.
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Pressure gradient has the same dimensions as that ofa)velocity gradientb)potential gradientc)energy gradientd)none of theseCorrect answer is option 'D'. Can you explain this answer?
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