Water is pumped at the rate of 0.075 m^3 / s from a reservoir 20 m above a pump to a free discha

Water is pumped at the rate of 0.075 m^3 / s from a...

Water is pumped at the rate of $0.075 \mathrm{m}^{3} / \mathrm{s}$ from a reservoir $20 \mathrm{m}$ above a pump to a free discharge $35 \mathrm{m}$ above the pump. The pressure on the intake side of the pump is $150 \mathrm{kPa}$ and the pressure on the discharge side is $450 \mathrm{kPa}$ All pipes are commercial steel of $15 \mathrm{cm}$ diameter. Determine (a) the head supplied by the pump and (b) the total head loss between the pump and point of free discharge.

Key Concepts

Bernoulli's Equation

Bernoulli's Equation is a statement of the conservation of energy for flowing fluids. It relates pressure, elevation (potential energy), and velocity (kinetic energy) along a streamline, allowing engineers to analyze changes in a fluid's energy as it flows through systems, including pumps and pipes.

Pressure Head

Pressure head is the height of a fluid column that produces a given pressure, defined by the ratio of the fluid pressure to the product of its density and gravitational acceleration. This concept enables the conversion of pressure differences into equivalent elevation differences, facilitating energy comparisons in fluid systems.

Pump Head

Pump head refers to the energy per unit weight that a pump adds to a fluid. It accounts for the elevation gain and pressure increase needed to overcome the gravitational, frictional, and other losses in a fluid system, essentially describing the work performed by the pump in moving the fluid from one point to another.

Head Loss

Head loss represents the reduction in the total head available in a fluid system due to friction, turbulence, and other dissipative effects within pipes, fittings, or other components. Understanding head loss is essential in designing systems to ensure that sufficient energy is provided by the pump to achieve the desired flow.

Flow Rate

Flow rate is the volume of fluid passing through a given cross-section of a pipe or system per unit time. It is crucial in determining the dynamic performance of a fluid system, as changes in flow rate can significantly affect the magnitude of frictional losses and the overall energy balance in the system.

Transcript

00:01 The net head supplied by the pump, net head supplied by the pump can be written as h -delta -h pump is equal to work done by pump, w -pump divided by the mass flow rate m.

00:17 So it can also be written as p divided by row plus alpha multiplied by b squared by 2 plus z -1, z.

00:26 This this is discharge discharge minus suction so p divided by row plus alpha v squared by 2 plus z this is suction now let us put some suffix for for the for the discharge side and suction side for discharge side discharge side discharge side suffix is 3 for for suction side the suffix is 2 hence we can write the above equation as delta delta as pump pump pump is equals to p3 divided by row plus alpha 3 multiplied by v3 divided by 2 plus z 3 x3 minus p2 divided by o plus alpha 2 multiplied by v2 square divided by z 2.

01:40 So this is this is our equation number 1.

01:46 Now the datum for 0 .2 and 0 .3 are same so so z2 will be equals to z3 will be equals to 0.

01:54 Also alpha 2 multiplied by v2 square is equal to alpha 3 multiplied by v2 square is equal to alpha 3, multiplied by v3 square is equal to alpha 4 multiple by v4 square.

02:04 Hence also the fluid is incomprehensible.

02:07 So, row density, row is equal to constant.

02:11 Hence, from all these values, we can write equation number one, h pump, delta h pump, is equal to p3 minus p2 divided by row.

02:24 Rest all term will be cancelled.

02:26 So we will put the value of p3 as 450 minus p.

02:30 P2 is written as given as 150 divided density is given as thousand.

02:35 So from here we get delta h pump.

02:38 We get delta h pump is equal to 0 .3 kilo -pascal meter per kg, which can be written as 300 newton meter per kg.

02:53 300 newton meter per kg...

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