Water is pumped through an inclined pipe. The pressure, velocity, and datum at the pipe inlet are 10 bar, 17 m/s, and 0 m, respectively. The pressure, velocity, and datum at the pipe outlet are 5 bar, 21 m/s, and 4 m, respectively. Assuming g=10 m/s2 for convenience, determine the change in the Bernoulli head in m for this section of the pipe. The kinetic energy correction factors may be approximated as 1.0 for simplicity.
Question
Water is pumped through an inclined pipe. The pressure, velocity, and datum at the pipe inlet are 10 bar, 17 m/s, and 0 m, respectively. The pressure, velocity, and datum at the pipe outlet are 5 bar, 21 m/s, and 4 m, respectively. Assuming g=10 m/s2 for convenience, determine the change in the Bernoulli head in m for this section of the pipe. The kinetic energy correction factors may be approximated as 1.0 for simplicity.
Solution
To solve this problem, we will use the Bernoulli equation, which states that the sum of the pressure head, velocity head, and elevation head is constant along a streamline. The Bernoulli equation is given by:
P1/ρg + V1²/2g + Z1 = P2/ρg + V2²/2g + Z2
where: P1 and P2 are the pressures at the inlet and outlet, respectively, V1 and V2 are the velocities at the inlet and outlet, respectively, Z1 and Z2 are the elevations at the inlet and outlet, respectively, ρ is the density of the fluid, and g is the acceleration due to gravity.
Given that the pressure is given in bar, we need to convert it to pascal (Pa) because 1 bar = 10^5 Pa. Also, the density of water is approximately 1000 kg/m³.
Substituting the given values into the Bernoulli equation, we get:
(1010^5 Pa)/(1000 kg/m³ * 10 m/s²) + (17 m/s)²/(210 m/s²) + 0 m = (510^5 Pa)/(1000 kg/m³ * 10 m/s²) + (21 m/s)²/(210 m/s²) + 4 m
Solving the above equation, we get:
1000 m + 14.45 m = 500 m + 22.05 m + 4 m
The change in the Bernoulli head is the difference between the total head at the outlet and the total head at the inlet, which is:
(500 m + 22.05 m + 4 m) - (1000 m + 14.45 m) = -488.4 m
Therefore, the change in the Bernoulli head for this section of the pipe is -488.4 m.
Similar Questions
Water flows at a rate of 0.035 m3/s in a horizontal pipe whose diameter is reduced from x cm to y cm by a reducer. If the pressure at the centerline is measured to be P1 kPa and P2 kPa before and after the reducer, respectively, determine the irreversible head loss in "meter unit" in the reducer. Take the kinetic energy correction factors to be 1.05. Take the density of water to be ρ = 1000 kg/m3. (Round the final answer to two decimal places.)Here,x=13 cmy=8 cmP1=492 kPaP2=432kPa
Water is flowing in a fire hose with a velocity of 1.0 m/s and a pressure of 200000Pa. At the nozzle the pressure decreases to atmospheric pressure (101300 Pa), thereis no change in height. Use the Bernoulli equation to calculate the velocity of thewater exiting the nozzle. (Hint: The density of water is 1000 kg/m3 and gravity g is9.8 m/s2. Pay attention to units!)]a.12 m/sb.13 m/sc.7m/sd. 14m/s
Water of density 1000 kg/m3 flows through a tube as shown in figure1a below.At section 1 the pressure is 200 kN/m2, the velocity is 5 m/s and the pipe diameter is0.12m. The pipe diameter at section 2 is 0.065m.Calculate: i) the velocity and pressure at section 2
Water is entering at pressure 4 × 104 pascal with a velocity of 2m/s in a horizontal pipe with cross-sectional area decreasing from 2 × 10–2 m2 to 0.01 m2 . The pressure at smaller cross-section of pipe in pascal will be :-323.43.4 × 1043.4 × 105
Water flows through a 1000 cm^2 pipe at 200 kg/s. Find the velocity, if the water is at 20 bar and 45 ℃.1 point2.0 m/s0.0002 m/s0.55 m/s5.5 m/s6.Question 6Consider a pump with a mass flow rate of wat
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.