Question

What pressure gradient along the streamline dP / ds, is requires to accelerate water upward in a vertical pipe at a rate of 30 ft/s2? What is the answer if the flow is downward?

Answer 1

Step-by-step explanation:

To accelerate water upward in a vertical pipe at a rate of 30 ft/s^2, we need to apply a pressure gradient along the streamline that is equal to the hydrostatic pressure gradient plus the pressure gradient due to acceleration.

The hydrostatic pressure gradient in a vertical pipe is given by dP/ds = ρg, where ρ is the density of water and g is the acceleration due to gravity.

Therefore, the pressure gradient required to accelerate water upward at a rate of 30 ft/s^2 is:

dP/ds = ρg + a

where a is the acceleration of the water. Substituting the values, we get:

dP/ds = (62.4 lbm/ft^3) x (32.2 ft/s^2) + 30 ft/s^2

dP/ds = 2,016.48 lbm/(ft s^2)

So, the pressure gradient required to accelerate water upward at a rate of 30 ft/s^2 is 2,016.48 lbm/(ft s^2).

If the flow is downward, the pressure gradient required to accelerate water downward at a rate of 30 ft/s^2 would be:

dP/ds = ρg - a

Substituting the values, we get:

dP/ds = (62.4 lbm/ft^3) x (32.2 ft/s^2) - 30 ft/s^2

dP/ds = 1,966.08 lbm/(ft s^2)

So, the pressure gradient required to accelerate water downward at a rate of 30 ft/s^2 would be 1,966.08 lbm/(ft s^2)