Flow through pipes

https://www.youtube.com/watch?v=D4MBL5QQQMI&list=PL2IEmUaKVY-g0nmNE5XL9YuDN0BzYIIhO&index=15 Each student go through one problem that is solved in this website and should practice it and work it one the board

Assignment 2&3

3rd Assignment problems Date of submission 14.11.2023 State Buckingham π theorem. The discharge of a centrifugal pump (q) is dependent on N (speed of pump), d (diameter of the impeller), g (Acceleration due to gravity), H (manometric head developed by the pump, and ρ and µ(density and dynamic viscosity of the fluid). Using the dimensional analysis and Buckingham π theorem, prove that it is given by Q=Nd^3 f(gH/(N^2 d^2 ),µ/(〖Nd〗^2 ρ)) Find an expression for the drag force on smooth sphere of diameter D, moving with uniform velocity v, in fluid density ρ and dynamic viscosity µ A 400 mm diameter pipe branches into two pipes of diameters 200mm and 250 mm respectively. If the average velocity in the 400 mm diameter pipe is 2.2m/s, evaluate the a) discharge of the pipe and b) the velocity in the 250 mm pipe, if the average velocity in 200mm pipe is 2.6m/s. Determine the length of an equivalent pipe of diameter 20cm and friction factor 0.02 for a given pipe system discharging 0.1m3/s. The pipe system consists of the following: A 10m line of 20cm diameter with f=0.03 Three 90-degree bend, k= 0.5 for each Two sudden expansion of diameter 20 to 30cm A 15m line of 30cm diameter with f=0.025 and A global valve fully open, k=10. A pipe 75mm diameter is 5m long and the velocity of flow of water in the pipe is 2.8m/s. If the central 2m length of pipe was replaced by 100mm diameter pipe and change of section be sudden. Calculate the loss of head and corresponding power saving. Take f=0.038 for the pipes of both diameters. Consider a situation where a turbulent flow (f=0.184 Re-0.2) of a fluid flowing through a square channel which has a smooth surface. Now the mean velocity of the fluid is doubled. Determine the change in the head loss of the fluid. Assume flow regime remains unchanged find (i) Head loss (ii) Minor losses Consider a case where in an engineering college having 1300 students and a reservoir is situated 12km away. The requirement is that water is to be supplied at the rate of 50 litres per head per day and half of the daily supply is to be pumped in 8 hours. If the head loss due to friction is 50 m, find the diameter of the pipe, Take f=0.004. Calculate the power required to maintain 0.06m3/s of oil (Specific gravity 0.75) through a steel pipe 300mm diameter and 1350m long. Take coefficient of friction f = 0.04 in the Darcy relation A pump is to supply 5 liters of water from a reservoir to a point 400m from the reservoir at the same level as the reservoir surface. Diameter of the pipe is 32mm and friction factor can be assumed as 0.0009. Calculate the power supplied by the pump to the water A pipe line 10km long delivers a power of 50kW at its outlet end. The pressure at inlet is 5000kN/m2 and the pressure drop per kilometer of pipe line is 50kN/m2. Find the size of the pipe and efficiency of transmission. Take 4f=0.02 The velocity of water in a pipe 200mm diameter is 5m/s. The length of the pipe is 500m. Find the loss of head due to friction, if f = 0.008 A sudden enlargement is introduced in a horizontal pipeline from 175mm diameter to 300mm diameter. Measurements indicate that when flow is from smaller to larger cross-section, the head loss is 0.6m in excess of that when the flow takes place from larger to smaller section. Determine the flow rate. Take the coefficient of contraction as 0.62 Water is flowing through a tapering pipe of length 200m having diameters 500mm at the upper end and 250 mm at the lower end, the pipe has a slope of 1 in 40. The rate of flow through the pipe is 250lit/sec. The pressures at the lower end and at the upper end are 20 N/cm2 and 10 N/cm2 respectively. Find the loss of head and direction of flow