THE UNIVERSITY OF THE WEST INDIES DEPARTMENT OF CIVIL ENGINEERING

CVNG 1001 - MECHANICS OF FLUIDS Problem Sheet #3 – Bernoulli’s Equation

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July 99 1(a) Show that the discharge over a rectangular sharp crested weir of width b is given by:

( )

−

+=

2/321

2/321

d g2u

g2uHxg2b

32CQ

where H is the head of water above the crest of the weir, ui is the velocity at a point in the channel upstream of the weir at which the flow may be considered uniform and parallel across the area of the channel, and Cd is the discharge coefficient of the weir. State all assumptions clearly. (b) A horizontal channel 3 m wide has a rectangular sharp crested weir of width 2 m with a crest elevation of 1.6 m measured from the bottom of the channel. If the depth of flow in the channel upstream of the weir is 2.5 m and the discharge coefficient of the weir is 0.60, determine the discharge over the weir to an accuracy of I%. July 97 A sharp-edged notch is in the shape of a symmetrical trapezium with a base of 0.6 m, a depth of 0.3 m and a top width of 1.2 m. Assuming a discharge coefficient of 0.6, determine from first principles the discharge through the notch when the water depth upstream of the notch is 0.25 m above the base of the notch. State all assumptions clearly.

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April 2002, # 2 A horizontal 20 cm diameter water pipe has in it a venturi-meter of throat diameter 12.5 cm, which is connected to a mercury manometer showing a difference of 87.8 cm. Find the velocity in the throat and the discharge. State all assumptions made. If the pressure before the venturi-meter is 800 kN/m2, what power would be given up by the water if it was allowed to discharge to atmospheric pressure immediately after the throat of the venturi-meter. (The specific gravity of mercury is 13.6.) April 2003, #3 Briefly explain how a Pitot tube is used to determine the velocity of a flow in a closed circular pipe flowing full. The figure below (drawn in class) shows a horizontal pipe of diameter 0.5 m that contracts to a diameter of 0.25 m. A piezometric tube is at Station 1, and a Pitot tube at Station 2. The tube has a fluid of relative density 0.8 and the difference in elevation in the water surfaces is 0.5 m. Determine the difference in the piezometirc head between Station 1 and Station 2. Hence determine the flow velocities of the water at Station 1 and Staion 2. If the upstream piezometric head is 4.0 m, find the piezometric head in the flow at Station 2.