What pressure would a 5000N weight of water exert at the bottom of a reservoir containing it if its length and breadth are 10m and 5m, respectively

Answer Details

Pressure measures how a force is spread over the surface it acts on: \[P = \frac{F}{A}.\] The water's weight, 5000 N, is the downward force pressing on the base of the reservoir, and the base is the rectangle on which that weight is distributed. So the whole problem is finding the base area and dividing.

The base area is \[A = \text{length} \times \text{breadth} = 10 \times 5 = 50\ \text{m}^{2},\] therefore \[P = \frac{5000}{50} = 100\ \text{N m}^{-2} = 100\ \text{Pa}.\] The pressure at the bottom of the reservoir is 100 Pa.

Notice that the depth of the water is never needed. Students often reach for \(P = \rho g h\) and stall because no depth or density is given, but that formula and \(P = F/A\) are the same statement: \(\rho g h\) is just the weight of the water column divided by the base area. When the weight of the liquid and the base dimensions are supplied, use \(F/A\) directly. Also check the units of the area: a pressure in pascals requires the area in square metres, so lengths given in centimetres must be converted before dividing.