- #1

lahanadar

- 22

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- TL;DR Summary
- Is there a way to change pressure in a duct that has a uniform cross sectional area regarding Bernoulli and continuity equations?

For a steady, non-viscous and incompressible flow, one can apply both Bernoulli's principle (no potentials) as

$$p+\frac{\rho v^2}{2} = p_t$$

where ##p##, ##\rho,##, ##v##, and ##p_t## are static pressure, density, flow velocity, and total pressure, respectively,

and continuitiy principle as

$$\rho vA=\dot m=Flow Rate$$

where ##A## is cross sectional area of the interest in the duct or stream tube.

From both of the equations above one can drive

$$p+\frac {k}{A^2}=cst$$

where ##k## is defined by ##k=\frac {\dot m^2}{2\rho}##.

From the last equation, it is implied that the only way of changing pressure is changing the cross sectional area. However, I worry that if there is an alternative way of changing the pressure without cross sectional area. In other words, is there a way to change pressure in a duct that has a uniform cross sectional area? (##A=cst##)

$$p+\frac{\rho v^2}{2} = p_t$$

where ##p##, ##\rho,##, ##v##, and ##p_t## are static pressure, density, flow velocity, and total pressure, respectively,

and continuitiy principle as

$$\rho vA=\dot m=Flow Rate$$

where ##A## is cross sectional area of the interest in the duct or stream tube.

From both of the equations above one can drive

$$p+\frac {k}{A^2}=cst$$

where ##k## is defined by ##k=\frac {\dot m^2}{2\rho}##.

From the last equation, it is implied that the only way of changing pressure is changing the cross sectional area. However, I worry that if there is an alternative way of changing the pressure without cross sectional area. In other words, is there a way to change pressure in a duct that has a uniform cross sectional area? (##A=cst##)