Calculate Absolute Pressure with Pump, Height, Density

[mindhater]

The drinking fountain outside your class shoots water 15 cm straight up in the air from a nozzle diameter of .58 cm. The pump at the base of the unit (90 m below the nozzle) pushes water into a 2.2 cm diameter supply pipe that goes up the nozzle. What is the absolute pressure provided by the pump?

i assume, it's calculate the pressure using (g)(h)(density) + atm pressure = absolute pressure

but I'm not sure...so if there's ne advice or something I'm missing...thx

 

[sickboy]

This one can be solved using Bernoulli's equation. There might be easier wayto do it, but this how I'd break it down (I suppose you are familiar the equation).

On the left side, there are pressure (supplied by the pump), velocity ( you can calculate by recognizing that A_1*v_1=A_2*v_2) and potential energy ( it makes sense to use this point as zero point for pot.energy). On the right side you have pressure again, velocity and potential energy.

There shouldn't be any unknowns remaining...

 

[M98Ranger]

You are correct in your approach to calculating absolute pressure using the formula (g)(h)(density) + atmospheric pressure. In this case, we can assume that the density of water is 1000 kg/m^3 and the acceleration due to gravity (g) is 9.8 m/s^2. We also need to take into account the atmospheric pressure, which is typically around 101,325 Pa.

First, we need to convert the given measurements into meters to match the units of our formula. The height of the pump is 90 m, the nozzle diameter is 0.58 cm (0.0058 m), and the supply pipe diameter is 2.2 cm (0.022 m).

Next, we can calculate the height (h) from the base of the pump to the nozzle using the Pythagorean theorem: h = √(90^2 + 0.0058^2) = 90.0005 m.

Now, we can plug in all the values into our formula: (9.8 m/s^2)(90.0005 m)(1000 kg/m^3) + 101,325 Pa = 901,800 Pa + 101,325 Pa = 1,003,125 Pa.

Therefore, the absolute pressure provided by the pump is 1,003,125 Pa, or approximately 10 atm. This pressure is the combined effect of the pump pushing water up the supply pipe and the natural atmospheric pressure pushing down on the water.

I hope this helps clarify the process for calculating absolute pressure in this scenario. If you have any further questions or concerns, please let me know.