Answer to Question #205702 in Mechanical Engineering for Welcome

Question

 A rigid tank initially under atmospheric pressure, contains oil (poil = 850 kg per metre cube) and water (Awater = 1000 kg per metre cube). Air is then charged into the tank to increase the total pressure up to 1 MPa gage. Determine the total downward movement of the free surface of the oil. Take average values of elastic bulk modulus for oil and water as 2050 MPa and 2075 MPa, respectively. Air 200 mm Oil 600mm Water 700 mm 300 mm 

Answer 1

$\rho{oil} = 850\ kg/m³\\ \rho{water} = 1000\ kg/m³\\$

$Total\ pressure=1MPa = 10⁶ \ Pa$

$Elastic\ modulus\ for\ oil= 2050\ Mpa = 2.05 ×10⁹Pa$

$Elastic\ modulus\ for\ water= 2075\ Mpa = 2.075×10⁹Pa$

$Air = 200mm = 0.2m\\ Oil = 600mm = 0.6m\\ Water =300mm = 0.3m$

P_oil = ρgh = 850 × 10 × 0.6 = 5100 Pa

P_water = 1000 × 10 × 0.3 = 3000 Pa

P_air = P - (P_oil + P_water)

P_air added = $1000000 - 5100 - 3000$ = $91900\ Pa$