question 1approximate the torque and power

Question

QUESTION 1

Approximate the torque and power necessary to rotate the inner 20 cm diameter cylinder shown in Figure 1. SAE 10W-30 oil at 20°C fills the gap. Assume a linear velocity profile.

QUESTION 2

Determine the height difference (H) shown in Figure.

QUESTION 3

A 4-m long curved gate is located in the side of a reservoir containing water as shown in Figure 3. Determine the magnitude of the horizontal and vertical components of the force of the water on the gate. (ρ_w=9810 N/m³)

QUESTION 4

A converging elbow (see Figure 4) turns water through an angle of 135^o in a vertical plane. The flow cross-section diameter is 400 mm at the elbow inlet, section (1), and 200 mm at the elbow outlet, section (2). The elbow flow passage volume is 0.2 m³ between sections (1) and (2). The water volume flowrate is 0.4 m³/s, and the elbow inlet and outlet gauge pressures are 150 and 90 kPa, respectively.

The elbow mass is 12 kg. Calculate the horizontal (x direction) and vertical (z direction) anchoring forces required to hold the elbow in place. Ignore viscous effects. (ρ_w=1000 kg/m³, g=9.81 m/s²)

QUESTION 5

Water flows into the sink shown in figure 5 at a flow rate of 8 L/min. If the drain is closed, the water will eventually flow through the overflow drain holes rather than over the edge of the sink. What is the minimum number of 1-cm diameter drain holes needed to ensure that the water does not overflow the sink? Neglect viscous effects.(w=1000 kg/m³, g=9.81 m/s²).