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Question #42100

Difficulty: 8/10 | 🟢 Free

The Question

Water of density $\rho = 1000 \text{ kg/m}^3$ flows steadily from a large pressurized tank into a horizontal pipe. The total absolute pressure in the tank is known exactly to be $P_0 = 5.0 \times 10^5 \text{ Pa}$ . The flow velocity in the pipe is measured as $v = 20 \text{ m/s}$ with a maximum relative error of $3.0\%$ . Assuming the density is exact and the fluid is ideal, what is the maximum percentage error in the calculated static pressure $P$ within the pipe?

Options

A.
$4.0\%$
B.
$6.0\%$
C.
$3.0\%$
D.
$2.4\%$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Bernoulli’s Energy Balance|Relative Error Propagation in Powers|Approximations

Why This Question Is Tricky

Common Mistakes

This question tests the non-linear propagation of relative errors in Bernoulli's equation.

A common trap is assuming the percentage error in static pressure equals either the velocity error ( $3\%$ ) or double the velocity error ( $6\%$ ) due to the $v^2$ term.

However, relative error depends on the absolute value of the specific quantity being calculated.

The differential relation $dP = -\rho v dv$ shows that the relative error in static pressure is $\frac{\Delta P}{P} = 2 \left(\frac{K.E.}{P}\right) \frac{\Delta v}{v}$ .

Students who blindly apply power rules without isolating the static pressure or who divide by the total pressure $P_0$ (yielding $2.4\%$ ) will select the incorrect options.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Mechanical Properties of Fluids - Class 11 Part 2
Concept	Bernoulli’s Energy Balance
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free