Question

Water from a tank is flowing down through a hole at its bottom with velocity 5 ms^-1. If this water falls on a flat surface kept below the hole at a distance of 0.1 m and spreads horizontally, the pressure (in kNm^-2) exerted on the flat surface is closest to
Given: acceleration due to gravity = 9.8 ms^-2 and density of water = 1000 kgm^-3

• A. 13.5
• B. 27.0
• C. 17.6
• D. 6.8

Answer 1

The Correct Option is B

To solve this problem, we can use the principle of conservation of momentum and the given data. The water flowing from the tank hits the flat surface, causing a change in momentum. We will calculate the force due to this change in momentum and then find the pressure exerted on the flat surface.

1. Understand the given data:
   • The velocity of water flowing out of the tank: \(v = 5 \, \text{ms}^{-1}\)
   • The height of the hole above the surface: \(h = 0.1 \, \text{m}\)
   • Density of water: \(\rho = 1000 \, \text{kgm}^{-3}\)
   • Acceleration due to gravity: \(g = 9.8 \, \text{ms}^{-2}\)
2. Calculate the mass flow rate: 

The volume of water hitting the surface per second depends on its velocity and cross-sectional area. Since the area is not provided, we calculate in terms of unit cross-sectional area.

The mass flow rate is given by:

\(\dot{m} = \rho \cdot A \cdot v\)

Where \(A\) is the cross-sectional area. For per unit area:

\(\dot{m} = \rho \cdot v = 1000 \cdot 5 = 5000 \, \text{kg/s (per unit area)}\)

1. Calculate the force exerted on the surface:

The force exerted by the water when it hits the surface is equal to the rate of change of momentum per second.

\(F = \dot{m} \cdot v = 5000 \cdot 5 = 25000 \, \text{N (per unit cross-sectional area)}\)

1. Calculate the pressure on the surface:

Pressure is defined as the force per unit area:

\(P = \frac{F}{A} = 25000 \, \text{N/m}^2 = 25 \, \text{kN/m}^2\)

1. Select the closest value from the provided options:

Comparing with given options, the closest value is \(27.0 \, \text{kN/m}^2\).

Therefore, the pressure exerted on the flat surface is closest to 27.0 kNm^-2.