By use of vector notation, determine the velocity of mass C, and the angular velocity of bar BC when Ɵ=30°.

Energy Equation Problem

9. If the blood viscosity is 2.7x10-3 Pa.s, length of the blood vessel is 1 m, radius of the blood vessel is 1 mm, calculate the tubular resistance of the blood vessel (in GPa.S/m3 ). If the blood pressure at the inlet of the above vessel is 43 mm Hg and if the blood pressure at the outlet of the above vessel is 38 mm Hg. Calculate the flow rate (in ml/min).

The water of a 14’ × 48’ metal frame pool can drain from the pool through an opening at the side of the pool. The opening is about h = 1.05 m below the water level. The capacity of the pool is V = 3740 gallons, the pool can be drained in t = 10.2 mins. P0 is the pressure of the atmosphere. ρ is the density of the water. a. Write the Bernoulli’s equation of the water at the top of the pool in terms of P0, ρ, h. Assuming the opening is the origin.  b. Write the Bernoulli’s equation of the water at the opening of the pool in terms of P0, ρ, h and v, where v is the speed at which the water leaves the opening. Assuming the opening is the origin.  c. Express v2 in terms of g and h.  d. Calculate the numerical value of v in meters per second.  e. Express the flow rate of the water in terms of V and t.  f. Express the cross-sectional area of the opening, A, in terms of V, v and t.  g. Calculate the numerical value of A in cm2

Question 3 Consider 2 which shows a pipe system connecting two reservoirs. The pipe diameter changes at point B as shown in the image A 10 cm 23 m NOT TO SCALE Figure 2: 9 m 6 cm с 3 m 1. Describe what is referred to by the hydraulic gradient line and the energy gradient line. What is the difference between the two levels? In what scenario will the energy and hydraulic grade lines coincide? 2. Calculate the velocities in the two segments of the pipe. Take into account the friction losses through the pipe, entry loss to the pipe and the shock contraction losses at B. Take the pipe friction factor as 0.005 and the coefficient of contraction at B as 0.6. 3. Draw the energy gradient line and the hydraulic gradient line for the system.

Water is stored in a tank sketched in the figure below to support the demand of a nearby community area.The system is designed so that pressure at the location B always lies in the range of 330 to 440 kPa (gauge).Water demand fluctuates between 0.3 and 1 m3/s regardless of pressure at B. The supply pipe of 600 mmdiameter and 1 km length between A and B is made of steel and has the equivalent sand roughness of 1 mm.Although not shown in the figure, the supply pipe has five 90◦ bends, each having the head loss coefficientof 0.8. The figure shows that the bottom end of the tank is located 42 m above the ground, and the pipe isburied 1.5 m below the ground. A pump system regulates so that the tank keeps the same water level all thetime. Assume water at 20◦C, and air in the storage tank has the atmospheric pressure. To meet the designcriterion for pressure at B, what should be the depth of water h in the storage tank?

Directions: In any clean sheet of paper, write your name, solve the problem and show your solution. Box your final answer. Take a picture of it and upload it here (image/pdf). 1) Between two sections in a vessel, a fluid moves in a steady flow manner. At entrance: A1=20 m2, P1=1300 kgm/m3. At exit: A2-10 m2, 02=0.00125 m /kg, Ü2=3 m/min. Determine the following: a) m, in kg/min b) Ủz in m/min

Determine the pressure drop over a reducer with the following conditions: Fluid density: 25 kg/m3Fluid velocity: 1.5 m/sFluid viscosity: 0.001 Pa*sInlet diameter: 0.12 mOutlet diameter: 0.019 mPipe absolute roughness: 4e-4 m Give your final answer in Pa, rounded to the nearest whole number. [Ignore entrance/exit losses and velocity loss terms]

Scenario 2:Water flows through a 2cm diameter pipe at 1.6m/s with kinematic viscosity of 1.31 × 10-6 m2/s and densityof 1000 kg/m3. Using the Buckingham Pi Theorem:f) Calculate the Reynolds number.g) Find the velocity required to give the same Reynolds number when the same pipe is transportingair.h) Obtain the ratio of pressure drops in the same length of pipe for both cases.i) Reflect on the case studies provided—Food Processing Industry, Chemical Manufacturing, and WaterTreatment Facilities. Evaluate how the dimensional analysis using the Buckingham PiTheorem applies to these scenarios and discuss the specific challenges encountered, suchas variable fluid properties and complex fluid dynamics which are not always captured by thetheorem. Offer practical recommendations for engineers to tailor dimensional analysistechniques to the unique requirements of each case study scenario, optimizing design andoperational efficiency.For air, the kinematic viscosity is 15.1 × 10-6 m2/s and the…

Example: What is the pressure at the center of the pipe B?