Problem 2: Control volume and Bernoulli Water drains from a tank through two r = 0.01 m diameter orifices: one located directly at the bottom of the tank, and the other at H/2. The tank has a diameter of R = 1m and the height of the water level is initially H = 1.5m. (1) Find the equations relating h and t for t t*. (2) Find the time, t*, it takes for the water level to drain to h(t*) = H/2. (3) Plot the relationship between the non-dimensional values (r/R)2√2g/H t (on the x-axis) and (on the y-axis) for t < t* and t> t*. R VH/2 h(t) → | H Figure 2: Draining tank with two orifices.

c) A nozzle is fastened to the end of a U-tube with dimensions as shown in Figure Q2c. The nozzle exhausts into atmospheric pressure at 100 kPa; neglect friction and compute the force exerted on the U-tube by the water. If the force required to hold the nozzle is 850 N, determine the inlet pressure. 5 CRN 31896 V = 1 m/s 5 cm diameter 1 cm diameter Figure Q2c

Q2/ Consider the following liquid level system shown below. The flow through the valve is related to the head (h) by the equation: 90 = ²/ √5³ Where: q.= the flow rate measured in (m³/min) h the head of liquid in (m) Suppose that the head is (4 m) at (t=0). Derive a relationship between the head and the time. 3m 6m 2.5m W 2m R * 9⁰

Q2/: As shown in the figure, the Assumptions of the flow through the venturi is steady, incompressible, irrational with negligible frictional effects , the effect of air column on the pressure change is negligible, the pressure can be assumed to be uniform at a given cross-section of the venturi meter and the flow is horizontal . Air is flowing through a venturi meter whose diameter is 2.6 in at the entrance part (location 1) and 1.8 in at the throat (location 2). The gage pressure is measured to be 12.2 psia at the entrance and 11.8 psia at the throat. Neglecting frictional effects, take the air density to be 0.075 lbm/ft. 1. Show that the volume flow rate can be expressed as: 2(P P2) | = A, p(1 – AŽIA}) 2. Find the flow rate of the air? 12.2 psia 11.8 psia Air 2.6 in 1.8 in

Q.4. In the system shown in figure, the water flow rate ,Q= 0.5 m3/s and pressure P=20 kPa are required at the point C. Calculate flow directions and flow rates in the pipes and power of the pump required in the system. Draw the energy lines in the system. Note: Neglect the local losses and take f=0.02 in the analysis. B ZA-20 m ZB=40 m 3 zc=4 m ZD=0 m A 2 Li=95 m, L2=120 m, L3=100 m 1 L2= 125m Pump D= 30 cm D k=0.046 mm

= constant Q16/ A pipe diameter of 400 mm carries water at a velocity of 25 m/s. The pressures at the points A and B are given as 29.43 N/cm² and 22.563 N/cm² respectively while the datum head at A and B are 28 m and 30 m. Find the loss of head between A and B. Z شكر الكائر 2B ADA=400 mm PA 29.43 N/cm #28 m ZA 28 Dg= 400 mm Pe = 22.563 N/cm ZB = 30 m DATUM LINE

Q2 = 10 liter/s DI =? Water D3 = 65mm Tank base area=1 m² rigure 5 (b) A water reservoir (p = 998 kg/m³ ) is being filled through section 1 at Vị = 3 m/s and through section 2 at Q. = 10 litre/s and exit at section 3 at 6.5 m/s which is shown in Figure 5. Calculate the diameter at section 1 so that : i. h is constant, ii. h decrease at 6 mm/s h is constant and section 2 is closed iii. of

Q4: Answer A or B A-Ethyl alcohol flows in the pipe as shown in Figure below of specific weight 49 Ib/ft'. What is the mass flow rate? If viscous effects are neglected. Take the specific weight for mercury equal to 846 and for water equal to 0 62.4 at 68° F. Mercury

From a very large tank with an absolute pressure of 3 bar, the water is discharged to the atmosphere by means of 2 smooth pipes of 100 m length, 1 m and 50 m long, connected in series. The height difference between the water level in the tank and the outlet is 50m, and the diameters of the pipes are 50mm and 100mm, respectively. In addition, a 500kPa turbine is placed on the 2nd Pipe. a) Draw the system roughly, show the dimensions on it.b) Calculate the exit velocity of the water from the 2nd pipe, ignoring the local losses.

20 m 10 m Figure 2: Schematic diagram of task 3. a. If the water volumetric flow is 0.005 m³/s and the pipe diameter is 10 cm, determine the Reynolds number in the pipe and the significance of this Information? b. Using Bernoulli's equation, find the water pressure at pipe inlet if the water is discharge to atmosphere at point B ?