Physics · Fluid Dynamics
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The speed v of a liquid leaving a tube depends on the change in pressure ΔP and the density ρ of the liquid. The speed is given by the equation. where k is a constant that has no units. What is the value of n?
- A
1/2
- B
1
- C
3/2
- D
2
Explanation is given in image.
This is the correct option. The equation for the speed of fluid flow, derived from Bernoulli's principle, is v = k(ΔP/ρ)1/2, indicating that the exponent n is 1/2.
This option is incorrect because it assumes a direct proportionality, which is not consistent with Bernoulli's equation where the speed is proportional to the square root of the pressure change divided by density.
This option is incorrect as it overestimates the relationship between speed and the physical parameters. The speed does not increase at this rate according to Bernoulli's principle.
This option is incorrect because it suggests a quadratic relationship, which is not supported by the principles of fluid dynamics where speed is proportional to the square root of the pressure change divided by density.
Tagged under Physics · Fluid Dynamics · 2018