A simple U tube manometer is used to measure the pressure of oil flowing in a pipeline. Its left limb is open to the atmosphere and the right limb is connected to the pipe. The center of the pipe is 70 mm below the level of mercury in the left limb. If the difference of mercury level in the two limbs is 144 mm, determine the gauge pressure of the oil in the pipe in Pascal. The specific gravity of the oil & mercury is 0.84 and 13.6 respectively.

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Dimensional homogeneity

The term dimensional homogeneity means that in an equation, the dimensions of each term on both sides are equal, which means the dimensions of the left-hand side (LHS) of an equation are similar to the dimensions of the right-hand side (RHS). For a dimensionally homogeneous equation, the powers of fundamental dimensions will be identical on both sides of the equation.