W05 Stepwise

Due date: Thursday 2/12, 11:59pm

Hydrostatic pressure

01

01

Fluid force on a triangular plate

Find the total force on the submerged vertical plate that is an isosceles triangle with (bottom) base $1\mathrm{m}$ and height $2\mathrm{m}$, and assume it is submerged with the upper vertex $3\mathrm{m}$ below the surface. Liquid is oil with density $\rho =900\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$.

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Solution

Solutions---0100-01

02

04

Fluid force on trapezoidal plates

For diagrams 1, 2, 3 (L to R) below, set up an integral to compute the hydrostatic force on the plate.

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Solution

Solutions---0100-04

Work performed

03

01

Pumping water from hemispherical tank

A hemispherical tank (radius $10\mathrm{m}$) is full of water. A pipe allows water to be pumped out, but requires pumping up $2\mathrm{m}$ above the top of the tank.

(a) Set up an integral that expresses the total work required to pump all the water out of the tank, assuming it is completely full.

(b) Now assume the tank start out full just to $6\mathrm{m}$. What does the integral become?

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Solution

Solutions---0120-01

04

02

Building a conical tower

Set up an integral that expresses the work done (against gravity) to build a circular cone-shaped tower of height $4\mathrm{m}$ and base radius $1.2\mathrm{m}$ out of a material with mass density $600\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$.

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Solution

Solutions---0120-02