Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 11 - Fluids - Problems - Page 310: 29

Answer

0.74 m

Work Step by Step

We can write, Pressure at the bottom of the container P, $P=P_{atm}+h_{w}\rho_{w}g+h_{m}\rho_{m}g-(1)$ Given that, $P=2P_{atm}$ & $h_{w}+h_{m} = 1\space m=>h_{w}=1-h_{m}$ (1)=> $2P_{atm}=P_{atm}+(1-h_{m})\rho_{w}g+h_{m}\rho _{m}g$ $P_{atm}-\rho_{w}g=h_{m}g(\rho_{m}-\rho_{w})$ $h_{m}=\frac{P_{atm}-\rho_{w}g}{g(\rho_{m}-\rho_{w})}$ ; Let's plug known values into this equation. $h_{m}=\frac{1.01\times10^{5}\space Pa-1000\space kg/m^{3}\times9.8\space m/s^{2}}{9.8\space m/s^{2}(13600\space kg/m^{3}-1000\space kg/m^{3})}=0.74\space m$
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