Question
Download Solution PDFA pressure gauge fitted on the side of a tank filled with liquid reads 50 kPa and 100 kPa at heights of 5 m and 10 m.
What is the approximate density of the liquid (in kg/m3)? (take g = 10)Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Hydrostatic pressure at any depth from the water surface is given by –
\(P = {\gamma _L}h = {\rho _L}gh\)
Where, γL = unit weight of liquid (N/m3),
ρL = density of liquid (Kg/m3),
g = acceleration due to gravity (m/sec2)
h = depth of location measured from water surface (m) and
P = Hydrostatic pressure (N/m2)
It should also be noted that the Pressure Gauges always reads the excess pressure from the surrounding.
Calculation:
Given,
\(g = 10\;m/se{c^2},\;{P_A} = 50kPa\;at\;5m\;and\;{P_B} = 100\;kPa\;at\;10m\)
\({P_A} = 50\; \times 1000\;N/{m^2} = \;{\rho _L} \times 10 \times 5 \Rightarrow {\rho _L} = 1000\;kg/{m^3}\)
\({P_B} = 100\; \times 1000\;N/{m^2} = \;{\rho _L} \times 10 \times 10 \Rightarrow {\rho _L} = 1000\;kg/{m^3}\)
∴ Density of liquid is 1000 kg/m3
Last updated on May 28, 2025
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