A cylindrical vessel is filled with water as shown in the figure. Calculate the difference in pressures due to water at points A and B. (Pressure due to air is negligible, density of water = g cm –3)
Answers
Answer:
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Step-by-step explanation:
By the end of this section, you will be able to:
Define pressure in terms of weight.
Explain the variation of pressure with depth in a fluid.
Calculate density given pressure and altitude.
If your ears have ever popped on a plane flight or ached during a deep dive in a swimming pool, you have experienced the effect of depth on pressure in a fluid. At the Earth’s surface, the air pressure exerted on you is a result of the weight of air above you. This pressure is reduced as you climb up in altitude and the weight of air above you decreases. Under water, the pressure exerted on you increases with increasing depth. In this case, the pressure being exerted upon you is a result of both the weight of water above you and that of the atmosphere above you. You may notice an air pressure change on an elevator ride that transports you many stories, but you need only dive a meter or so below the surface of a pool to feel a pressure increase. The difference is that water is much denser than air, about 775 times as dense.
Answer:
Its bottom supports the weight of the fluid in it. Let us calculate the pressure exerted on the bottom by the weight of the fluid. That pressure is the weight of the fluid mg divided by the area A supporting it (the area of the bottom of the container):
P
=
m
g
A
.
We can find the mass of the fluid from its volume and density:
m = ρV.
The volume of the fluid V is related to the dimensions of the container. It is
V = Ah,
where A is the cross-sectional area and h is the depth. Combining the last two equations gives
m
=
ρ
A
h