Question

Question: Two thin-walled drinking glasses having equal base areas but different shapes, with very different cross sectional areas above the base, are filled to the same level with water. According to the expression , the pressure is the same at the bottom of both glasses. In view of this equality, why does one weigh more than the other?

Short answer

The small base area is exerted due to the downward component adds up to an extra downward force.

Step-by-step solution

Step 1: Bernoulli’s equation

The sum of the pressure, kinetic energy per unit volume, and gravitational potential energy per unit volume has the same value at all points along a streamline for an ideal fluid. This result is summarized in Bernoulli’s equation:

P+$\frac{1}{2}\rho V^2+\rho gh=cons\tan t$

Where

P= Pressure of fluid

V= Volume of fluid

$\rho =$Density of fluid

h= Height of fluid in pipe

Find why one weighs more than the other

A B

Fromconceptwehavetheequation P+$\frac{1}{2}\rho V^2+\rho gh=cons\tan t$.

While it is given in the question the expression P= P₀+$\rho gh=cons\tan t$

Are same,

Thetotalvolumeofwaterintheglass is dependent on the Weight.

Thewaterpushesonlyhorizontallyonthesidewallsanddoesnotcontributestoanextradownwardforceabovethatfeltbythebase., thepressureatthebottomis dependentonlyonthedepthwithcylindricalglass,by seeing figureA,

Ontheotherhandiftheglasswideatthetopwithconicalshapethewaterpushesoutwardanddownwardoneachbitofsidewall by seeing figureB.

The small base area is exerted due to the downward component adds up to an extra downward force.