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Exercise:
Consider the flow of a liquid through a hole in the bottom of a container. If ht is the height of the liquid above the hole then the velocity of the liquid emerging from the hole will be given by v cgh^/ where g is the acceleration of gravity ncg and c is an empirical constant which is about . in many cases. The rate of change of the volume of liquid in the tank is dfracmathrmdvmathrmdt -av -acgh^/ where a is the cross-sectional area of the hole. Using the fact that V _^h Ah mathrmdh where Ah is the cross-sectional area of the tank at a height h show that dfracmathrmdhmathrmdt -dfracacgh^/Ah. This result is known as Torricelli's law.

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Exercise:
Consider the flow of a liquid through a hole in the bottom of a container. If ht is the height of the liquid above the hole then the velocity of the liquid emerging from the hole will be given by v cgh^/ where g is the acceleration of gravity ncg and c is an empirical constant which is about . in many cases. The rate of change of the volume of liquid in the tank is dfracmathrmdvmathrmdt -av -acgh^/ where a is the cross-sectional area of the hole. Using the fact that V _^h Ah mathrmdh where Ah is the cross-sectional area of the tank at a height h show that dfracmathrmdhmathrmdt -dfracacgh^/Ah. This result is known as Torricelli's law.

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container, de, dgl, differental, equation, law, liquid, physics, torricelli
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(5, default)
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6 (default)
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ENG (English)
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Calculative / Quantity
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