Question

3(b) Bernoulli's equation states that P+ pgh-const (i) Explain what each of the three terms on the left hand side of the equation represents. What is the physical interpretation of this equation? 151 The surface pressure on Venus is 92 atm, and the acceleration due to gravity is 0.894g. A space mission leaves a cylindrical tank of benzene standing upright on the planet's surface. The tank is sealed and is pressurised so that the pressure inside the tank at its top is 92 atm. The tank has a diameter of 1.72 m and is 11.5 m tall. You may take the density of benzene to be 900 kg/m', and that 1 atm 1.013x10 Pa. (i) What total force is exerted on the inside surface of the bottom of the tank? 161 ) What force doesthe Veusian amosphere exert on the uside surface of the bottmhtnk2 (iii) A Venusian robber knocks a horizontal pipe into the bottom of the tank to drain off the benzene. What is the speed of the benzene as it leaves the tank? (You may ignore any effects due to drag.) 161 (iv) If the robber raises the tank by 0.5 m, how much time after leaving the tank does it take the benzene to hit the ground? What horizontal distance does the benzene cover in this time? 161

Answer 1

The Bernoulli equation describes the behavior of a fluid that moves along a pipe, pipe, channel, etc. It states that in a fluid where there is no viscocity or friction (ideal fluid) that circulates through a closed conduit, the energy that the fluid possesses remains constant along the path.

The Bernoulli equation is made up of three components or contributions:

1. Kinetics:

$\frac{1}{2}\rho v^{2}$

Describe the energy that is caused by the speed of the fluid that passes through the duct.

2.  Potential

$\rho gh$

Describe the energy due to the altitude of the fluid that passes through the duct.

3. Pressure

$P$

Describe the energy that a fluid contains due to the force it exerts on the area.

The sum of these magnitudes is constant at any point of the conduit.