Answer :
Final answer:
The pressure at a depth of 4.5m in the given sludge is found to be 1013.4 kN/m^2. This can also be expressed as 2076408.384 pounds per square foot (psf), or 147.008 pounds per square inch (psi).
Explanation:
The specific weight of sludge given is expressed as W = 0.200 + 50h in kN/m3. For a depth of 4.5m, the specific weight of the sludge would be W = 0.200 + 50*4.5 = 225.200 kN/m3.
To find the pressure at this depth, we could simply multiply the specific weight by the depth, hence P = W*h = 225.200 kN/m3 * 4.5m = 1013.4 kN/m2. Now to express this in psf (pounds per square foot) and psi (pounds per square inch), we would need to convert the kN/m2 (1 kN/m2 = 2048.16 psf = 0.1450377377 psi) so P = 1013.4 kN/m2 * 2048.16 psf/kN/m2 = 2076408.384 psf and P = 1013.4 kN/m2 * 0.1450377377 psi/kN/m2 = 147.008 psi.
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