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A U-tube is made up of two capillaries of diameters 1.0 mm and 1.5 mm respectively. The U tube is kept vertically and partially filled with water of surface tension 0.0075kg/m and zero contact angles.
Calculate the difference in the level of the menisci caused by the capillarity.
Calculate the difference in the level of the menisci caused by the capillarity.
Correct answer is '1 mm'. Can you explain this answer?
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A U-tube is made up of two capillaries of diameters 1.0 mm and 1.5 mm ...
Problem Statement: A U-tube is made up of two capillaries of diameters 1.0 mm and 1.5 mm respectively. The U tube is kept vertically and partially filled with water of surface tension 0.0075kg/m and zero contact angles.Calculate the difference in the level of the menisci caused by the capillarity.
Solution:
Step 1: Calculate the capillary rise in the two tubes.
Capillary rise, h = (2T cosθ) / (ρgd)
where T is the surface tension of water (0.0075 kg/m), θ is the contact angle (zero in this case), ρ is the density of water (1000 kg/m³), g is the acceleration due to gravity (9.81 m/s²), and d is the diameter of the tube.
For the tube with diameter 1.0 mm, h = (2*0.0075*cos0)/(1000*9.81*0.001) = 0.015 mm
For the tube with diameter 1.5 mm, h = (2*0.0075*cos0)/(1000*9.81*0.0015) = 0.01 mm
Step 2: Calculate the difference in the level of the menisci.
The difference in the level of the menisci is equal to the difference in the capillary rise in the two tubes.
Difference in the level of the menisci = 0.015 - 0.01 = 0.005 mm
Therefore, the difference in the level of the menisci caused by the capillarity is 0.005 mm or 1 mm (rounded off to the nearest whole number).
Final Answer: The difference in the level of the menisci caused by the capillarity is 1 mm.
Solution:
Step 1: Calculate the capillary rise in the two tubes.
Capillary rise, h = (2T cosθ) / (ρgd)
where T is the surface tension of water (0.0075 kg/m), θ is the contact angle (zero in this case), ρ is the density of water (1000 kg/m³), g is the acceleration due to gravity (9.81 m/s²), and d is the diameter of the tube.
For the tube with diameter 1.0 mm, h = (2*0.0075*cos0)/(1000*9.81*0.001) = 0.015 mm
For the tube with diameter 1.5 mm, h = (2*0.0075*cos0)/(1000*9.81*0.0015) = 0.01 mm
Step 2: Calculate the difference in the level of the menisci.
The difference in the level of the menisci is equal to the difference in the capillary rise in the two tubes.
Difference in the level of the menisci = 0.015 - 0.01 = 0.005 mm
Therefore, the difference in the level of the menisci caused by the capillarity is 0.005 mm or 1 mm (rounded off to the nearest whole number).
Final Answer: The difference in the level of the menisci caused by the capillarity is 1 mm.
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A U-tube is made up of two capillaries of diameters 1.0 mm and 1.5 mm respectively. The U tube is kept vertically and partially filled with water of surface tension 0.0075kg/m and zero contact angles.Calculate the difference in the level of the menisci caused by the capillarity.Correct answer is '1 mm'. Can you explain this answer?
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