6.20) Calculate the density of a fluid in which a hydrometer of uniform density 0.80g/cm^3 floats with 90% of its volume submerged.
Note: Pls provide me an answer with relative solution/formula to this problem. Thanks!
the volume of fluid with the same mass as the hydrometer
... is 90% of the volume of the hydrometer
density = mass / volume
... for the hydrometer ... m / v = 0.80 g/cm^3
... for the fluid ... m / (.9 v) = (m / v) / .9 = (.80 / .9) g/cm^3
To calculate the density of the fluid, we can use the principle of flotation. The principle of flotation states that when an object floats in a fluid, the weight of the fluid displaced by the object is equal to the weight of the object itself.
In this case, the hydrometer is floating in the fluid, so the weight of the fluid it displaces is equal to the weight of the hydrometer. The weight of the hydrometer can be calculated by multiplying its volume by its density and the acceleration due to gravity:
Weight of hydrometer = volume of hydrometer x density of hydrometer x acceleration due to gravity
Since 90% of the volume of the hydrometer is submerged, we can express the volume of the hydrometer in terms of its submerged volume:
Volume of hydrometer = Submerged volume / 0.9
The weight of the fluid displaced by the hydrometer is equal to the weight of the hydrometer:
Weight of fluid displaced = weight of hydrometer
The weight of the fluid displaced can be calculated by multiplying the volume of the fluid displaced by its density and the acceleration due to gravity:
Weight of fluid displaced = volume of fluid displaced x density of fluid x acceleration due to gravity
Since the hydrometer is floating, the volume of the fluid displaced is equal to the volume of the hydrometer:
Volume of fluid displaced = Submerged volume
Setting the weight of the fluid displaced equal to the weight of the hydrometer, we have:
volume of fluid displaced x density of fluid x acceleration due to gravity = volume of hydrometer x density of hydrometer x acceleration due to gravity
Canceling out the terms of acceleration due to gravity and rearranging the equation, we get:
density of fluid = (volume of hydrometer x density of hydrometer) / volume of fluid displaced
Plugging in the given values, we have:
density of fluid = (volume of hydrometer x 0.80g/cm^3) / volume of fluid displaced
Simplifying further, we can express the density of fluid in g/cm^3 as:
density of fluid = 0.80g/cm^3 x (volume of hydrometer / volume of fluid displaced)
By substituting the given values for the volume of hydrometer and the volume of fluid displaced, you can calculate the density of the fluid.