Final answer:
To accelerate water upward, a negative pressure gradient along the streamline dp/ds is required, which means the pressure will decrease in the direction of flow.
Step-by-step explanation:
To accelerate water upward, a pressure gradient along the streamline dp/ds is required. In a streamline flow, the pressure decreases in the direction of flow due to the increase in velocity.
The Bernoulli's equation can be applied to determine the pressure gradient. The equation is given as:
P + 0.5ρv2 + ρgh = constant
Where P is the pressure, ρ is the density of the fluid, v is the velocity, g is the acceleration due to gravity, and h is the height of the fluid.
Since we want to accelerate the water upward, the velocity v will increase. This means the pressure P will decrease in the direction of flow. Therefore, the pressure gradient along the streamline dp/ds will be negative.