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  1. Pressure. Pressure (p) is defined as the normal force F per unit area A over which the force is applied, or \[p = \frac{F}{A} \ldotp \label{14.3}\] To define the pressure at a specific point, the pressure is defined as the force dF exerted by a fluid over an infinitesimal element of area dA containing the point, resulting in p = \(\frac{dF}{dA}\).

  2. P = hρg. (11.4.6) (11.4.6) P = h ρ g. This value is the pressure due to the weight of a fluid. Equation 11.4.6 11.4.6 has general validity beyond the special conditions under which it is derived here. Even if the container were not there, the surrounding fluid would still exert this pressure, keeping the fluid static.

  3. The answer is yes. This seems only logical, since both the water’s weight and the atmosphere’s weight must be supported. So the total pressure at a depth of 10.3 m is 2 atm—half from the water above and half from the air above. We shall see in Pascal’s Principle that fluid pressures always add in this way.

  4. The volume of the fluid V V is related to the dimensions of the container. It is. V = Ah, V = Ah, where A A is the cross-sectional area and h h is the depth. Combining the last two equations gives. m = ρAh. m = ρ Ah. If we enter this into the expression for pressure, we obtain. P = (ρAh)g A. P = (ρ Ah) g A.

  5. 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 ...

  6. The pressure gauge on her air tank reads \(6.9 \times 10^6 \, Pa\). What force does the air inside the tank exert on the flat end of the cylindrical tank, a disk 0.150 m in diameter? Strategy. We can find the force exerted from the definition of pressure (Equation \red{pressure}) provided we can find the area \(A\) acted upon. Solution

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  8. The answer is yes. This seems only logical, since both the water’s weight and the atmosphere’s weight must be supported. So the total pressure at a depth of 10.3 m is 2 atm—half from the water above and half from the air above. We shall see in Pascal’s Principle that fluid pressures always add in this way.

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