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Chapter 3: Problem 109

A bowl is inverted symmetrically and held in a dense fluid, \(\mathrm{SG}=15.6,\) to a depth of \(200 \mathrm{mm}\) measured along the centerline of the bowl from the bowl rim. The bowl height is \(80 \mathrm{mm},\) and the fluid rises \(20 \mathrm{mm}\) inside the bowl. The bowl is \(100 \mathrm{mm}\) inside diameter, and it is made from an old clay recipe, \(\mathrm{SG}=6.1 .\) The volume of the bowl itself is about \(0.9 \mathrm{L}\) What is the force required to hold it in place?

Short Answer

Expert verified
The force required to hold the bowl in place can be calculated using the four steps outlined above. It involves calculating the mass and weight of the bowl, the buoyancy force exerted by the fluid, and finally, the difference between the weight of the bowl and buoyancy force will give the required force.

Step by step solution

01

Calculate mass of the bowl

The specific gravity (SG) is a dimensionless quantity defined as the ratio of the density of the material to the density of water at a specified temperature. We can calculate the mass of the bowl by multiplying the specific gravity by the volume and the density of water (1000 kg/m鲁): \(mass_{bowl} = SG_{bowl} * V_{bowl} * density_{water}\).
02

Calculate weight of the bowl

The weight of the bowl can be calculated by multiplying the mass of the bowl by gravitational acceleration (9.81 m/s虏): \(weight_{bowl} = mass_{bowl} * gravity\).
03

Calculate buoyancy force

Buoyancy force or upthrust is the upward force exerted by a fluid that opposes the weight of an immersed object. It is equal to the weight of the fluid displaced by the body. As the bowl is inverted and submerged, the fluid is inside and outside of the bowl, so we calculate total fluid weight displaced by the bowl and the fluid inside the bowl: \(buoyancy_{force} = (SG_{fluid} * V_{fluid_displaced} * density_{water} * gravity) + (SG_{fluid} * V_{fluid_inside} * density_{water} * gravity)\).
04

Calculate force required to hold the bowl in place

The force required to hold the bowl in place will be the difference between the weight of the bowl and the buoyancy force: \(Force_{required} = weight_{bowl} - buoyancy_{force}\).

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