A regional water service checks the pressure in pipes supplied by an elevated storage tank. Fig. 1 is a simplified diagram of the system. Gauge L is beside ...
Question 1 Report
A regional water service checks the pressure in pipes supplied by an elevated storage tank. Fig. 1 is a simplified diagram of the system. Gauge L is beside a workshop near the valley floor. Gauge H is at a clinic on higher ground. The water surface in the tank is 36 m above gauge L and 14 m above gauge H. Take the density of water as 1000 kg/m3 and take g as 10 N/kg. Ignore atmospheric pressure.
(a) State which gauge, L or H, has the greater water pressure. [1]
(b) Calculate the pressure caused by the water at gauge L. [3]
(c) Explain why the pressure at gauge H is less than the pressure at gauge L. [2]
(d) Calculate the difference in water pressure between the two gauges. [3]
Answer Details
(a) Gauge L has the greater water pressure because it has a greater depth of water above it. [1]
(b) \[p=h\rho g=36\text{ m}\times1000\text{ kg/m}^3\times10\text{ N/kg}\] [1]
\[p=360\,000\text{ Pa}=360\text{ kPa}\]
The pressure at L is 360 000 Pa or 360 kPa. [2]
(c) Gauge H has a smaller depth, or shorter vertical column, of water above it. [1] The water above a unit area therefore has less weight and exerts less force per unit area, so H has lower pressure. [1]
(d) The depth difference is:
\[36-14=22\text{ m}\] [1]
\[\Delta p=22\text{ m}\times1000\text{ kg/m}^3\times10\text{ N/kg}\] [1]
\[\Delta p=220\,000\text{ Pa}=220\text{ kPa}\]
The pressure difference is 220 000 Pa or 220 kPa. [1]
Download The App On Google Playstore
Everything you need to excel in your exams
