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Because gasoline is less dense than water, drums containing gasoline will float in water. Suppose a 210-L steel drum is completely full of gasoline. What can the total volume of steel be used in making the drum if the gasoline-filled drum is to float in freshwater?

Short Answer

Expert verified

The total volume of steel used to make the drum if the gasoline-filled drum is to float in freshwater is 9.9 x 10-3m3.

Step by step solution

01

Understanding the principle of buoyancy

Buoyancy is an upward force exerted by the fluid in the upward direction that opposes the weight of a fully or partially submerged body. It is expressed in Newtons.

02

Identification of the given data

The volume of the gasoline in the steel drum is Vgasoline = 210L.

03

Determination of the total volume of steel

As the steel drum is filled with gasoline, the buoyancy force (FB) will be equal to the sum of the weight of the steel drum (Wsteel) and weight of gasoline (Wgasoline) filled inside it.


Here, msteeland mgasoline is the mass of the steel drum and gasoline respectively. And we know that the mass and volume ratio equals density. Thus, mass can be written as the product of volume and density.

Here, Vgasolineand Vsteel are the volume of gasoline and steel drum respectively. Ρgasoline, ρsteel and ρwater are the densities of gasoline, steel and water respectively.

Rearranging,

04

Calculations to determine the desired result

Substitute the standard values of densities, that are, Ρgasoline= 680 kg/m3, ρsteel= 7800 kg/m3and ρwater= 1000 kg/m3, in the above formula.

Hence, the total volume of steel used to make the drum if the gasoline-filled drum is to float in freshwater is 9.9 x 10-3m3.

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(a) Show that the flow speed measured by a venturi meter (see Fig. 10-29) is given by the relation

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Figure 10-56

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