Question

Given P space equals space P subscript 0 space plus space rho g h, your objective is to determine the uncertainty of P by measuring P subscript 0 comma space rho comma space g space and space h , What is the expression for capital delta P subscript g , that is, the g's contributing term for the overall uncertainty of P

Answer 1

Answer:

the g's contributing term for the overall uncertainty of P is  $dP_g = [\frac{dg}{g}]$

Step-by-step explanation:

From the question we are told that

   The pressure is   $P = P_o + \rho gh$

The first step in determining the uncertainty of P in by obtaining the terms in the equation contributing to it uncertainty and to do that we take the Ln of both sides of the equation

    $ln P = lnP_o + ln(\rho gh )$

=>   $ln P = lnP_o + ln \rho + ln g + ln h$

Then the next step is to differentiate both sides of the equation

    $\frac{d(ln P)}{dP} = \frac{d(ln P_o)}{dP_o} + \frac{d(ln \rho)}{d\rho} +\frac{d(ln g)}{dg} + \frac{d(ln h)}{dh}$

=>    $\frac{dP}{P} = \frac{dP_o}{P_o} + \frac{d \rho}{\rho} +\frac{d g}{g} + \frac{d h}{h}$

We asked to obtain the contribution of the term g to the uncertainty of P

This can deduced from the above equation as

     $dP_g = [\frac{dg}{g}] P$