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In a mercury differential manometer used for measuring pressure differences across a venturimeter in a water pipeline, if an error of 2 mm has been made in observing a differential head of 10 mm, the percentage error in pressure difference is:
  • a)
    12.6
  • b)
    25.2
  • c)
    20
  • d)
    2
Correct answer is option 'C'. Can you explain this answer?
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Given data:
Differential head observed (h) = 10 mm
Error in observation = 2 mm

The pressure difference can be calculated using the formula:
ΔP = ρgh

Where,
ρ = density of mercury
g = acceleration due to gravity
h = differential head

Calculation:
Let's assume the density of mercury as 13,600 kg/m³ and acceleration due to gravity as 9.81 m/s².

The actual pressure difference can be calculated as:
ΔP_actual = ρgh
= 13600 * 9.81 * 10⁻³ * 10
= 1331.56 Pa

The observed differential head is 10 mm, but there is an error of 2 mm.
Therefore, the actual differential head is:
h_actual = h_observed - error
= 10 - 2
= 8 mm

The actual pressure difference can also be calculated using the actual differential head as:
ΔP_actual = ρgh_actual
= 13600 * 9.81 * 10⁻³ * 8
= 1065.25 Pa

The percentage error in pressure difference can be calculated using the formula:
% Error = (|ΔP_actual - ΔP_observed| / ΔP_actual) × 100

Substituting the values, we get:
% Error = (|1065.25 - 1331.56| / 1065.25) × 100
= 20.01%

Therefore, the percentage error in pressure difference is 20%. Hence, option C is the correct answer.
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In a mercury differential manometer used for measuring pressure differences across a venturimeter in a water pipeline, if an error of 2 mm has been made in observing a differential head of 10 mm, the percentage error in pressure difference is:a)12.6b)25.2c)20d)2Correct answer is option 'C'. Can you explain this answer?
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