What is the density of the unknown green fluid, of the blue fluid is water (density 1000 kg/m3) and the heights shown here are y = 3.40 cm and h = 7.00 cm?
What is the density of the unknown green fluid, of the blue fluid is water (density 1000 kg/m3) and the heights shown here are y = 3.40 cm and h = 7.00 cm?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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What is the density of the unknown green fluid, of the blue fluid is water (density 1000 kg/m3) and the heights shown here are y = 3.40 cm and h = 7.00 cm?
![**Problem Statement:**
**What is the density of the unknown green fluid, if the blue fluid is water (density 1000 kg/m³) and the heights shown here are \( y = 3.40 \, \text{cm} \) and \( h = 7.00 \, \text{cm} \)?**
**Visual Description:**
The image depicts a U-tube manometer containing two immiscible fluids: one green and the other blue. The blue fluid is water. The green fluid, whose density is unknown, is present on the left side of the U-tube, while the blue water is on the right side.
**Given Measurements:**
- The height of the green fluid column (\( h \)) is \( 7.00 \, \text{cm} \).
- The height of the displaced water column (\( y \)) is \( 3.40 \, \text{cm} \).
**Additional Information:**
- The density of water is \( 1000 \, \text{kg/m}^3 \).
**Required Calculation:**
Using the principle of hydrostatics, the pressure at the bottom of both columns must be equal due to the fluid being at equilibrium.
Using the heights and densities, one can set up the following equation:
\[ \rho_{\text{green fluid}} \cdot g \cdot h = \rho_{\text{water}} \cdot g \cdot y \]
where:
- \(\rho_{\text{green fluid}}\) is the density of the green fluid (unknown).
- \(\rho_{\text{water}} = 1000 \, \text{kg/m}^3 \) is the density of water.
- \(g\) is the acceleration due to gravity (common on both sides and thus cancels out).
- \(h = 7.00 \, \text{cm} \) is the height of the green fluid.
- \(y = 3.40 \, \text{cm} \) is the height of the water column.
Solving for \(\rho_{\text{green fluid}}\):
\[ \rho_{\text{green fluid}} = \rho_{\text{water}} \cdot \frac{y}{h} \]
\[ \rho_{\text{green fluid}} = 1000 \, \text{kg/m}^3 \cdot \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57b84c9f-5371-4bf5-98f4-a4910a16e225%2F368d33b5-5df9-4e4c-a1a4-3c09e050ebd8%2Fakbulyf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
**What is the density of the unknown green fluid, if the blue fluid is water (density 1000 kg/m³) and the heights shown here are \( y = 3.40 \, \text{cm} \) and \( h = 7.00 \, \text{cm} \)?**
**Visual Description:**
The image depicts a U-tube manometer containing two immiscible fluids: one green and the other blue. The blue fluid is water. The green fluid, whose density is unknown, is present on the left side of the U-tube, while the blue water is on the right side.
**Given Measurements:**
- The height of the green fluid column (\( h \)) is \( 7.00 \, \text{cm} \).
- The height of the displaced water column (\( y \)) is \( 3.40 \, \text{cm} \).
**Additional Information:**
- The density of water is \( 1000 \, \text{kg/m}^3 \).
**Required Calculation:**
Using the principle of hydrostatics, the pressure at the bottom of both columns must be equal due to the fluid being at equilibrium.
Using the heights and densities, one can set up the following equation:
\[ \rho_{\text{green fluid}} \cdot g \cdot h = \rho_{\text{water}} \cdot g \cdot y \]
where:
- \(\rho_{\text{green fluid}}\) is the density of the green fluid (unknown).
- \(\rho_{\text{water}} = 1000 \, \text{kg/m}^3 \) is the density of water.
- \(g\) is the acceleration due to gravity (common on both sides and thus cancels out).
- \(h = 7.00 \, \text{cm} \) is the height of the green fluid.
- \(y = 3.40 \, \text{cm} \) is the height of the water column.
Solving for \(\rho_{\text{green fluid}}\):
\[ \rho_{\text{green fluid}} = \rho_{\text{water}} \cdot \frac{y}{h} \]
\[ \rho_{\text{green fluid}} = 1000 \, \text{kg/m}^3 \cdot \
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