Calculate Absolute Pressure with Pump, Height, Density

  • Thread starter mindhater
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In summary, the drinking fountain outside the class has a nozzle diameter of .58 cm and shoots water 15 cm straight up from a pump located 90 m below the nozzle. Using Bernoulli's equation, the absolute pressure provided by the pump can be calculated by considering the pressure, velocity, and potential energy on both sides of the equation. This method can be used to determine the absolute pressure without any remaining unknowns.
  • #1
mindhater
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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
 
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  • #2
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 [itex] A_1*v_1=A_2*v_2 [/itex]) 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...
 
  • #3


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.
 

1. How do you calculate absolute pressure?

To calculate absolute pressure, you need to know three variables: pump pressure, height, and density. The formula for calculating absolute pressure is: Absolute Pressure = Pump Pressure + (Density x Height x 9.8). This formula takes into account the pressure exerted by the weight of the fluid due to gravity.

2. What is pump pressure?

Pump pressure is the pressure exerted by a pump on a fluid. It is typically measured in units of pressure, such as pounds per square inch (psi) or pascals (Pa).

3. How does height affect absolute pressure?

The higher the height, the greater the weight of the fluid, and therefore, the higher the absolute pressure. This is because the weight of the fluid increases as it is pulled down by gravity.

4. What is the role of density in calculating absolute pressure?

Density is the mass per unit volume of a substance. In the formula for calculating absolute pressure, density is multiplied by height, which takes into account the weight of the fluid due to gravity. Therefore, density plays a crucial role in determining the absolute pressure of a fluid.

5. What are some examples of situations where absolute pressure is important to calculate?

Absolute pressure is important to calculate in a variety of fields, such as engineering, meteorology, and chemistry. Some specific examples include calculating the pressure at the bottom of a water tank, determining the atmospheric pressure at a certain altitude, and measuring the pressure inside a chemical reactor.

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