Roman 2

Roman thermae around the year 200 were baths equipped with underground central heating. The largest of them had a rectangular swimming pool with cold water, the bottom dimensions were 17m and 51m, the water reaches a height of 150 cm. Calculate according to Pascal's law:

a/water pressure at the bottom of the pool,
b/pressure force acting on the bottom of the pool

Correct answer:

p =  14715 Pa
F =  12757905 N

Step-by-step explanation:

$$\begin{gathered} a=17\text{m} \\ b=51\text{m} \\ c=150\text{cm}\to \text{m}=150:100\text{m}=1.5\text{m} \\ {S}_1=a\cdot b=17\cdot 51=867{\text{m}}^2 \\ \rho =1000{\text{kg/m}}^2 \\ g=9.81{\text{m/s}}^2 \\ p=\rho \cdot g\cdot c=1000\cdot 9.81\cdot 1.5=14715\text{Pa} \end{gathered}$$

$F=p\cdot S_1=14715\cdot 867=12757905\text{N}$

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