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Pharos University ME 259 Fluid Mechanics for Electrical Students Revision for Mid-Term Exam Dr. A. Shibl

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2 Manometer Example Determine the pressure at point A in the figure below if h 1 = 0.2 m and h 2 = 0.3 m. Use water = 1000 kg/m 3. Solution: P 2 = P 1 + Hg gh 2 But P 1 = P atm (open to atmosphere) ==>P 1 = 0 (gauge) P 2 = Hg gh 2 P 3 = P A + water g(h 1 +h 2 ) We know that P 2 = P 3 (same horizontal level) Thus Hg gh 2 = P A + water g(h 1 +h 2 ) P A = Hg gh 2 - water g(h 1 +h 2 ) P A = 13.54x1000x9.81x0.3 – 1000x9.81x( ) P A = 39, P A = 34.9 kPa (gauge) Points to be selected: 1 – at the open end of the manometer 2 – at the right leg of the manometer 3 – same level with point 2 but at left leg of the manometer 4 – same level as point A Pressure at the points: P 1 =P atm P 2 = P 3 P 4 = P A

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Static Force Example A rectangular gate of dimension 1 m by 4 m is held in place by a stop block at B. This block exerts a horizontal force of 40 kN and a vertical force of 0 kN. The gate is pin-connected at A, and the weight of the gate is 2 kN. Find the depth h of the water.

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Continuity Example Water flows steadily through a nozzle. The nozzle diameter at the inlet is 5 cm, and the diameter at the exit is 3cm. The average velocity at the inlet is 4 m/s. What is the average velocity at the exit? V 1 A 1 = V 2 A 2

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Bernoulli Equation

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Water moving through Venture nozzle reaches a low pressure at section 1. Nozzle dimensions are d 1 = 3 mm, d 2 = 9 mm, and h = 150 mm. Determine the minimum possible water speed (V2) at the exit of the nozzle so that fluid will be drawn up the suction tube.

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Momentum Equation For Steady Flow ΣF x = ṁ (V2—V1) x

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A water jet with a velocity of 30 m/s impacts on a splitter plate so that 1/4 of the water is deflected toward the bottom and 3/4 toward the top. The angle of the plate is 45 o. Find the force required to hold the plate stationary. Neglect the weight of the plate and water, and neglect friction.

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