Question

What gauge pressure must a machine produce in order to suck mud of density 1800 kg/m³up a tube by a height of 1.5 m?

Short answer

Gauge pressure to suck the mud is

Step-by-step solution

The given data

1. Density of mud,$p=1800\mathrm{kg}/{\mathrm{m}}^3$
2. Height of the tube,$h=1.5m$

Understanding the concept of hydrostatic pressure

We can use the formula for hydrostatic pressure in terms of density, gravitational acceleration, and height to solve for gauge difference. Hydrostatic pressure is that, which is exerted by a fluid at any point of time at equilibrium due to the force applied by gravity.

Formula:

Net pressure applied on a fluid surface,$∆p=pgh$ (i)

Calculation of gauge pressure

Gauge pressure to suck the mud can be found using equation (i) and the given values as:

$$\begin{gathered} ∆p=-1800\times 9.8\times 1.5 \\ =-2.6\times {10}^{4}Pa \end{gathered}$$

Hence, the pressure required is$-2.6\times {10}^{4}Pa$