(1) A fluid of constant density flows at the rate of 15 Liters/ sec along a pipe AB of 100 mm diameter. This pipe branches at B into two pipes, BC and BD each of 25mm diameter and a third pipe BE of 50mm diameter. The flow rates are such that the flow through BC is three times the flow rate through BE and the velocity through BD is 4 m/s. Find the flow rates in the three branches BC, BD and BE and the velocities in pipes AB, BC and BE. Water is flowing through a pipe with a velocity of 7.2 m/s. Express this velocity as velocity head in meters of water. What is the corresponding pressure in kN/m2.

DIFFERENT QUESTION FOR REVISON-EXAMINATION

Additional Questions:

(1) A fluid of constant density flows at the rate of 15 Liters/ sec along a pipe AB of 100 mm diameter. This pipe branches at B into two pipes, BC and BD each of 25mm diameter and a third pipe BE of 50mm diameter. The flow rates are such that the flow through BC is three times the flow rate through BE and the velocity through BD is 4 m/s. Find the flow rates in the three branches BC, BD and BE and the velocities in pipes AB, BC and BE.

Water is flowing through a pipe with a velocity of 7.2 m/s. Express this velocity as velocity head in meters of water. What is the corresponding pressure in kN/m².

(2) A pipe of 150mm bore is delivering water at a rate of 7500dm³/min at a pressure of 820 kN/m².It connects by a gradually expanding pipe to a main of 300 mm bore which runs 3 m above it. The main is designed to withstand a maximum pressure of 814 kN/m². Neglecting loses due to friction determine if the main will fail or not.

What pressure should the main withstand if it is to have a factor of safety of 1.5.

(3) Water flows form a reservoir into a closed tank in which the pressure is 70 kN/m² below atmospheric. If the water level in the reservoir is 6 m above that in the tank, find the velocity of the water entering the tank, neglecting friction.

(4) A vertical pipe conveying water tapers from 50 mm in diameter at the top to 25 mm in diameter at the bottom in a length of 1.8 m. a pressure gauge is connected to the top section and a second pressure gauge is connected at the bottom section. When 0.194 m³vof water per minute flows up the pipe the gauges shows a pressure difference of 31kN/m². Determine the quantity of water which must flow downwards through the pipe if the gauges are to show no pressure difference and the frictional loses are assumed to vary as the square of the velocity.

(5) In a vertical pipe conveying water, pressure gauges A and B are inserted where the diameters are 150 mm and 75mm respectively. Point B is 2.4 m below A and when the rate of flow down the pipe is 21dm³/s the pressure at B is 12kN/m² greater than at A. assuming that the loses in the pipe between A and B can be can be expressed as kv²/2g where v is the velocity at A, find the value of k.

If the gauges at A and B are replaced by tubes filled with water and connected to a U-tube manometer containing mercury of specific gravity 13.6 give a sketch showing how the levels in the two limbs will different, hence calculate the value of this difference measured in milliliters.

(6) With the aid of a sketch, describe the venture meter and explain its mode of action.

(7) Provide a description of difference between a venture meter and an orifice plate.

(8) Derive an expression for the theoretical discharge of a venturi meter and show how it can be modified to give the actual discharge.

(9) A venturi meter tapers from 300 mm in diameter at the entrance to 100 mm in diameter at the throat, and the coefficient of its discharge is determined as 0.98. A differential mercury U tube gauge is connected between pressure tappings at the entrance and the throat. The venturi meter is used to measure the flow of water, and water fills the leads to the U-tube and is in contact with the mercury. The difference of level in the U-tube is 55 mm. The intended water flow rate is 0.05 m³/s; show if the indeed flow is reached or not.

(10) A horizontal venturi meter measures the flow of oil of specific gravity of 0.9 in a 75 mm diameter pipe line. If the difference of pressure between the full bore and the throat tappings is 34.5 kN/m² and the area ratios of the two sections is 4,  calculate the rate of flow assuming a coefficient of discharge of 0.97.