Pressure difference when height changes

In summary, the problem asks for the difference in pressure (in atmospheres) that the blood vessels in a giraffe's head have to accommodate as the head is lowered from a full upright position to ground level for a drink. The equation for this is given as ΔP=pgΔh, where ΔP represents the difference in pressure, p is the density of the fluid, g is the acceleration due to gravity, and Δh is the change in height. The given equation P=Po + pgh is for calculating absolute pressure, not the difference in pressure. The solution for this problem is calculated as ΔP=pgΔh= (1.05x10^3 kg/m^3) x 9.
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Homework Statement



Calculate the difference in pressure (in atmospheres) that the blood vessels in a giraffe's head have to accommodate as the head is lowered from a full upright position to ground level for a drink. The height of an average giraffe is about 6m.
(Note I'm currently only looking for the answer is Pascals)


Homework Equations



I thought the equation was P=Po + pgh
but the answer just says P=pgh

Po= 101000Pa

The Attempt at a Solution



P=Po + pgh
P=101000 + (1.05x10^3 kg/m^3) x 9.8 x 6m
P=162.740Pa

But the answer gives...

ΔP=pgΔh
[itex]\frac{ΔP}{Po}[/itex] = [itex]\frac{pgΔh}{Po}[/itex]
= [itex]\frac{(1.05\times103)\times9.8\times6}{1.013\times105}[/itex]
=0.609Pa

I don't understand why they've rearranged the equation the way they have and exactly how they are using it. It just doesn't seem right.
Can someone please explain?
 
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  • #2
I thought the equation was P=Po + pgh

I don't think so. this is the equation for absolute pressure.
The problem asks for difference in pressure.
 

1. What is pressure difference when height changes?

The pressure difference when height changes refers to the change in pressure experienced by a fluid as it moves from one height to another. This is due to the force of gravity acting on the fluid, causing it to exert different pressures at different heights.

2. How does pressure change with height?

As height increases, the pressure decreases. This is because the weight of the fluid above a certain height decreases, leading to a decrease in the force of gravity acting on it. As a result, the pressure exerted by the fluid decreases.

3. What is the equation for calculating pressure difference when height changes?

The equation used to calculate pressure difference when height changes is P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height difference between two points.

4. How does pressure change in a fluid at rest?

In a fluid at rest, the pressure is constant at any particular height. This is because the weight of the fluid above a certain height is evenly distributed, leading to an equal force of gravity acting on all points at that height. Therefore, the pressure remains constant.

5. What factors can affect the pressure difference when height changes?

The pressure difference when height changes can be affected by several factors, including the density of the fluid, the acceleration due to gravity, and the height difference between two points. Additionally, the presence of other forces, such as wind or temperature gradients, can also influence the pressure difference.

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