Formula sheet No explanation is made on purpose Do not assume that you need to use every formula In this test always assume that K entrance = 0.5, K exit =1, K bend = 0.25 If the flow in the pipe is in fully developed turbulence In direction along contact surface In this test assume that You are expected to know the Energy, and Momentum balances In a two dimensional velocity field If C = 0 velocity can be expressed in terns of a velocity potential If D= 0 velocity can be expressed in terns of a stream function Power At 100% eff =

Calculate the average capillary rise of water (  = 9810 N/m 3 ) between two vertical plates spaced 1mm apart. (  = N/m) The plate one the left is normal glass with a contact angle of 0 o The plate on the right is surface treated glass with a contact angle of 60 0 Voller 1 Capillary force F, balance weight of liquid W For unit width into page

Voller 2 The figure shows the cross-section of a submerged hinged gate ( weight 100 kN) in water (  = 9810 N/m 3 ). The gate has an area of A = 4 m 2 And a geometry such that the centroid axis (parallel to the hinge and into the page) is a slant distance 2 m below the hinge and The line of action of the center of pressure is a slant distance of 2.5 m below the hinge Determine the height of water h required to just open the gate h

Voller 3 The water (  = 1000 kg/m 3 ) in a jet of area A = 0.05 m 2 is deflected by a cone. If an external horizontal force of F x = -1kN (acting to the left) is applied to the cone Calculate, assuming the cone moves in the horizontal direction, the magnitude of the velocity of the cone relative to the water jet (i.e., the value of V jet -V cone ) Momentum balance

turbine 10 m 110 m A B Voller 4 Water (  = 9810 N/m 3 ) flows from Tank A to Tank B at discharge of Q = 1 m 3 /s Through a pipe of Length 1000 m Diameter 0.5 m Surface roughness 0.1 mm Before entering Tank B the water is directed through a turbine with an 80% efficiency Assuming that the flow in the pipe is fully developed turbulence and approximating the Cross section as = 0.2 m 2 calculate the power drawn from the turbine. K entrance = 0.5, K exit =1, K bend = 0.25 Power At 100% eff = Energy from A to B