Flow work and energy for continuous fluid flow is calculated as $Pv$

This is explained in terms of the rest of the fluid pushing the back of a fluid element in consideration, which is described in terms of a hypothetical piston.

In a solved example involving air flowing uniformly and steadily, my textbook essentially uses the ideal gas law to solve for the rate of energy transport by mass. They write, $h=C_pT$ and $E=\frac{dm}{dt}(h+ke)$ since they have consolidated $u+Pv = h$ & neglected gravitational PE, and then they plug in values.

What I don't get is, these calculations are done for a "static" gas. The fact that it's flowing here doesn't seem to be accommodated for. Wouldn't the pressure $P$ used in calculating the flow energy have to include the additional force due to the liquid flowing?

EDIT: Here's how flow energy is defined and explained by my text

Flow work and energy for continuous fluid flow is calculated as $Pv$

This is explained in terms of the rest of the fluid pushing the back of a fluid element in consideration, which is described in terms of a hypothetical piston.

In a solved example involving air flowing uniformly and steadily, my textbook essentially uses the ideal gas law to solve for the rate of energy transport by mass. They write, $h=C_pT$ and $E_{rate}=\frac{dm}{dt}(h+ke)$ since they have consolidated $u+Pv = h$ & neglected gravitational PE, and then they plug in values.

What I don't get is, these calculations are done for a "static" gas. The fact that it's flowing here doesn't seem to be accommodated for. Wouldn't the pressure $P$ used in calculating the flow energy have to include the additional force due to the liquid flowing?

EDIT: Here's how flow energy is defined and explained by my text

And also energy transport:

Flow work and energy for continuous fluid flow is calculated as $Pv$

This is explained in terms of the rest of the fluid pushing the back of a fluid element in consideration, which is described in terms of a hypothetical piston.

In a solved example involving air flowing uniformly and steadily, my textbook essentially uses the ideal gas law to solve for the rate of energy transport by mass. They write, $h=C_pT$ and $E=\frac{dm}{dt}(h+ke)$ since they have consolidated $u+Pv = h$ & neglected gravitational PE, and then they plug in values.

What I don't get is, these calculations are done for a "static" gas. The fact that it's flowing here doesn't seem to be accommodated for. Wouldn't the pressure $P$ used in calculating the flow energy have to include the additional force due to the liquid flowing?

Flow work and energy for continuous fluid flow is calculated as $Pv$

This is explained in terms of the rest of the fluid pushing the back of a fluid element in consideration, which is described in terms of a hypothetical piston.

In a solved example involving air flowing uniformly and steadily, my textbook essentially uses the ideal gas law to solve for the rate of energy transport by mass. They write, $h=C_pT$ and $E=\frac{dm}{dt}(h+ke)$ since they have consolidated $u+Pv = h$ & neglected gravitational PE, and then they plug in values.

What I don't get is, these calculations are done for a "static" gas. The fact that it's flowing here doesn't seem to be accommodated for. Wouldn't the pressure $P$ used in calculating the flow energy have to include the additional force due to the liquid flowing?

EDIT: Here's how flow energy is defined and explained by my text

Flow work and energy for continuous fluid flow is calculated as $Pv$

This is explained in terms of the rest of the fluid pushing the back of a fluid element in consideration, which is described in terms of a hypothetical piston.

In a solved example involving air flowing uniformly and steadily, my textbook essentially uses the ideal gas law to solve for the rate of energy transport by mass. They write, $h=C_pT$ and $E=\frac{dm}{dt}(h+ke)$ since they have consolidated $u+Pv = h$ and then they plug in values.

What I don't get is, these calculations are done for a "static" gas. The fact that it's flowing here doesn't seem to be accommodated for. Wouldn't the pressure $P$ used in calculating the flow energy have to include the additional force due to the liquid flowing?

Flow work and energy for continuous fluid flow is calculated as $Pv$

This is explained in terms of the rest of the fluid pushing the back of a fluid element in consideration, which is described in terms of a hypothetical piston.

In a solved example involving air flowing uniformly and steadily, my textbook essentially uses the ideal gas law to solve for the rate of energy transport by mass. They write, $h=C_pT$ and $E=\frac{dm}{dt}(h+ke)$ since they have consolidated $u+Pv = h$ & neglected gravitational PE, and then they plug in values.

What I don't get is, these calculations are done for a "static" gas. The fact that it's flowing here doesn't seem to be accommodated for. Wouldn't the pressure $P$ used in calculating the flow energy have to include the additional force due to the liquid flowing?