Water at 20degc in the pressurized tank at 75 kpa gage

Question

Q1. Water at 20°C, in the pressurized tank at 75 kPa gage, flows out and creates a vertical jet as shown. Assuming steady frictionless flow:

1) What is the pressure at point 1, 2 and 3?

2) What is the velocity at point 2?

3) Determine the maximum height H to which the jet rises.

4) Would the height to which the jet rises be more in case of a viscous fluid?

Q2. For the horizontal pipe reducing section shown, D₁ = 8 cm, D₂ = 5 cm, and p₂ = 101 kPa = p_atm. All fluids are at 20°C. If V₁ = 5 m/s and the manometer reading is h = 58 cm, compute the following:

a) The pressure difference indicated by the manometer, in Pa (gage).

b) The velocity of the now at location 2, in m/s.

c) The total horizontal force resisted by the bolts in the flange.

Q3. A cylindrical water tank discharges through a well-rounded orifice to hit a plate, as shown in the Figure below. Water flows out through the orifice and impinges on the plate horizontally and splits equally in the vertical direction. The force F shown in the figure is in the horizontal direction. g acts along the vertical direction. The flow is inviscid. Assume that the direction and velocity of flow does not change as water flows from the orifice to the plate.

(a) Now assume that D (diameter of the tank) is much higher than d (diameter if the orifice/jet) such that the level of water in the tank (h) changes very little with time. If, under such circumstances, the force F required to hold the plate is 40 N, what is the depth h?

(b) Now assume that that D(diameter of the tank) is comparable to the d (diameter if the orifice/jet) such that the level of water in the tank (h) changes at the rate of 2.5 cm every second. If, under such circumstances, the force F required to hold the plate is 40 N. what is the tank diameter D?

Show the CV used to do the force balance.

Q4. An incompressible liquid jet of velocity V_j and area A_j strikes a single 180° bucket on a turbine wheel rotating at a constant angular velocity U. The turbine has no angular acceleration. Neglect the effect of gravity. Also assume that the size of the bucket is very small compared to the turbine wheel of radius R and hence every point of the bucket can be assumed to be moving at the same velocity. Assuming steady state operation, the bucket to be a moving CV with constant velocity and the flow to be inviscid:

a) Find an expression for the power P delivered.

b) At what Ω is the power a maximum?