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So assume a pressure-driven, incompressible, and steady flow in $x$-direction between 2 inf. fixed surfaces.

Why should the partial derivative $dP/dx$$\frac{\partial P}{\partial x}$ in the Navier-Stoke eqnStokes Eqn. be constant?

My understanding is that:

  1. not 0, since it's driving the flow
  2. constant to, so there is no accelacceleration (steady)

But howwhy is it that a constant dP/dx$\frac{\partial P}{\partial x}$ maintains the velocity?

Wouldn't the pressure difference b/t$\frac{dp}{dt}$ at each $x$ point act a force on the flow, and thus accelerate the flow?

So assume a pressure-driven, incompressible, and steady flow in $x$-direction between 2 inf. fixed surfaces.

Why should the partial $dP/dx$ in the Navier-Stoke eqn. be constant?

My understanding is that:

  1. not 0 since it's driving the flow
  2. constant to so no accel (steady)

But how is it that a constant dP/dx maintains the velocity?

Wouldn't the pressure difference b/t each $x$ point act a force on the flow, thus accelerate the flow?

So assume a pressure-driven, incompressible, and steady flow in $x$-direction between 2 inf. fixed surfaces.

Why should the partial derivative $\frac{\partial P}{\partial x}$ in the Navier-Stokes Eqn. be constant?

My understanding is that:

  1. not 0, since it's driving the flow
  2. constant, so there is no acceleration (steady)

But why is it that a constant $\frac{\partial P}{\partial x}$ maintains the velocity?

Wouldn't the pressure difference $\frac{dp}{dt}$ at each $x$ point act a force on the flow and thus accelerate the flow?

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So assume a pressure driven-driven, incompressible, and steady flow in $x$-direction between 2 inf. fixed surface,surfaces.

Why should the partial $dP/dx$ in the Navier-Stoke eqn. be constant?

My understanding is that:

  1. not 0 since it's driving the flow
  2. constant to so no accel (steady)

But how is it that a constant dP/dx maintainmaintains the velocity?

Wouldn't the pressure difference b/t each $x$ point act a force on the flow, thus accelerate the flow?

So assume a pressure driven, incompressible, and steady flow in $x$-direction between 2 inf. fixed surface,

Why should the partial $dP/dx$ in the Navier-Stoke eqn be constant?

My understanding is that:

  1. not 0 since it's driving the flow
  2. constant to so no accel (steady)

But how is it that a constant dP/dx maintain the velocity?

Wouldn't the pressure difference b/t each $x$ point act a force on the flow, thus accelerate the flow?

So assume a pressure-driven, incompressible, and steady flow in $x$-direction between 2 inf. fixed surfaces.

Why should the partial $dP/dx$ in the Navier-Stoke eqn. be constant?

My understanding is that:

  1. not 0 since it's driving the flow
  2. constant to so no accel (steady)

But how is it that a constant dP/dx maintains the velocity?

Wouldn't the pressure difference b/t each $x$ point act a force on the flow, thus accelerate the flow?

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Qmechanic
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Flow in x direction$x$-direction and pressure driven velocity

So assume a pressure driven, incompressible, and steady flow in x$x$-direction between 2 inf. fixed surface,

Why should the partial dP/dx$dP/dx$ in the Navier-Stoke eqn be constant?

My understanding is that:

  1. not 0 since it's driving the flow
  2. constant to so no accel (steady)

But how is it that a constant dP/dx maintain the velocity?

Wouldn't the pressure difference b/t each x$x$ point act a force on the flow, thus accelerate the flow?

Flow in x direction and pressure driven velocity

So assume a pressure driven, incompressible, and steady flow in x-direction between 2 inf. fixed surface,

Why should the partial dP/dx in the Navier-Stoke eqn be constant?

My understanding is that:

  1. not 0 since it's driving the flow
  2. constant to so no accel (steady)

But how is it that a constant dP/dx maintain the velocity?

Wouldn't the pressure difference b/t each x point act a force on the flow, thus accelerate the flow?

Flow in $x$-direction and pressure driven velocity

So assume a pressure driven, incompressible, and steady flow in $x$-direction between 2 inf. fixed surface,

Why should the partial $dP/dx$ in the Navier-Stoke eqn be constant?

My understanding is that:

  1. not 0 since it's driving the flow
  2. constant to so no accel (steady)

But how is it that a constant dP/dx maintain the velocity?

Wouldn't the pressure difference b/t each $x$ point act a force on the flow, thus accelerate the flow?

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