Final answer:
The pressure at a certain point in a pipe can be found using Bernoulli's equation, which relates pressure, density, height difference, and velocity of the fluid.
Step-by-step explanation:
The correct answer is option D: |P2 - P1| = (ρgΔh + ½ ρv22).
To find the pressure at a certain point in a pipe, we can use Bernoulli's equation, which relates the pressure, density, height difference, and velocity of the fluid. In this case, the pressure at a point in the pipe is given by the difference between the pressures at two different points:
|P2 - P1| = (ρgΔh + ½ ρv22)
where P2 is the pressure at the higher point, P1 is the pressure at the lower point, ρ is the density of the fluid, g is the acceleration due to gravity, Δh is the height difference, and v is the velocity of the fluid.
The correct answer is option theoretical head of a centrifugal pump when the number of blades is infinite. To begin with, the theoretical head (H) can be found using Euler's turbomachinery equation, given as H = (U2*Vθ2 - U1*Vθ1)/g,
where U is the tangential component of velocity at the corresponding diameter, Vθ is the tangential component of absolute velocity of the fluid, and g is the acceleration due to gravity.
In the case of an infinite number of blades, the fluid does not slip and thus the tangential component of the absolute velocity (Vθ) at the outlet can be calculated using the outlet angle β2 and the tangential velocity of the wheel U2, with a similar approach for the inlet using β1 and U1.
For this specific problem, you will calculate the U and Vθ values using the given diameters, angles, and flow rate, and then apply them to Euler's equation to compute the theoretical head. This operation will involve applying principles from fluid dynamics, as well as basic kinematic equations to find the velocities involved.