Can anyone help me with thisBernoulli qn?

[gunblaze]

A water tank springs a leak at a certain position called position 2. The pressure at position 2 is equal to the atmospheric pressure(100KPa) and at another position called position 1 the pressure is 500KPa in excess of atmospheric pressure. What is the velocity of escape of the water at the leak? It may be assumed that the velocity of the water at the leak is much greater than the velocity at position 1. (density of water=1000Kgm-3)

Thx

 

[Andrew Mason]

A water tank springs a leak at a certain position called position 2. The pressure at position 2 is equal to the atmospheric pressure(100KPa) and at another position called position 1 the pressure is 500KPa in excess of atmospheric pressure. What is the velocity of escape of the water at the leak? It may be assumed that the velocity of the water at the leak is much greater than the velocity at position 1. (density of water=1000Kgm-3)

If the pressure at position 2 is the same as the atmospheric pressure, an opening at position 2 will not produce a leak. The velocity of the water at the leak is 0. Better check the question again.

AM

 

[gunblaze]

no.. the total pressure at position 2 is 200KPa. The pressure at position 2, neglecting air pressure, is 100KPa. note: the total pressure at postion 1 is 500KPa.

 

[gunblaze]

what i want to know is that by having 2 unknown velocity, v at position 1 and v at position 2, how can i find the velocity at position 2?

 

[Andrew Mason]

what i want to know is that by having 2 unknown velocity, v at position 1 and v at position 2, how can i find the velocity at position 2?

If the tank is large, the velocity at position 2 is independent of the pressure at position 1. The speed of the water at position 2 is determined by Bernouilli's equation:

$$\frac{1}{2}\rho v_0^2 + P_0 = \frac{1}{2}\rho v'^2 + P'$$

Where P_0 = 200 KPa, v_0 = 0; P' = 100 KPa

Just solve for v'.

AM

[note: I changed the 1 and 2 subscripts to avoid confusion with the positions]

 

[gunblaze]

If the tank is large, the velocity at position 2 is independent of the pressure at position 1.

erm.. May i know why?

thx!

 

[Andrew Mason]

erm.. May i know why?

thx!

Because the velocity at position 2 is determined by the pressure at position 2. Pressure is energy per unit volume. The increase in kinetic energy of water comes from the potential energy stored as water pressure. Why would its energy be determined by the pressure anywhere else?

AM