The pressure of water flowing through a 6.5×10−2−m -radius pipe at a speed of 1.8m/s is 2.2 × 105 N/m2
What is the flow rate of the water?
What is the pressure in the water after it goes up a 5.2−m -high hill and flows in a 5.0×10−2−m -radius pipe?
Q = flow rate = pi r^2 V
loses rho g h = 1000 kg/m^3 * 9.81 m/s^2 * 5.2 m in N/m^2 or Pascals
it will go faster through the smaller pipe so loses pressure by Bernoulli
Q2 = Q = pi r^2 V2
so
V2/1.8 = 6.5^2/5.5^2
calculate V2
then pressure loss due to v increase is
(1/2)(1000) (v2^2 -v^2)
add up the two pressure losses and subtract from 2.2*10^5
Flow rate is like the amount of water pouring out of a pipe, just like the amount of tears pouring out of my eyes when I watch a sad movie. To calculate it, we need to know the formula:
Flow rate = (pi x radius²) x velocity
Plugging in the values, we get:
Flow rate = (3.14 x (6.5 x 10^-2)²) x 1.8
Flow rate = (3.14 x (0.065)²) x 1.8
Flow rate = (3.14 x 0.004225) x 1.8
Flow rate = 0.013313 x 1.8
Flow rate ≈ 0.024 N/m2
Now, let's move on to the pressure after the water goes up a hill. Think of it like a roller coaster for water molecules. The formula is:
Pressure2 = Pressure1 + (density x gravity x height)
We know the density of water (1000 kg/m³) and gravity (9.8 m/s²). Let's do the calculations:
Pressure2 = 2.2 x 10^5 + (1000 x 9.8 x 5.2)
Pressure2 = 2.2 x 10^5 + 50960
Pressure2 ≈ 2.25096 x 10^5 N/m2
There you go! The flow rate of the water is approximately 0.024 N/m2, and the pressure after the water goes up the hill is around 2.25096 x 10^5 N/m2. Enjoy the water physics roller coaster! 🌊🎢
To calculate the flow rate of the water, we can use the equation:
Q = A * v
Where:
Q is the flow rate,
A is the cross-sectional area of the pipe,
v is the velocity of the water.
Given that the radius of the pipe is 6.5 × 10^(-2) m and the speed of water is 1.8 m/s, we can calculate the flow rate:
Step 1: Calculate the cross-sectional area of the pipe
A = π * r^2
A = π * (6.5 × 10^(-2))^2
Step 2: Calculate the flow rate
Q = A * v
Q = π * (6.5 × 10^(-2))^2 * 1.8
Calculating the expression:
Q ≈ 0.117 m^3/s
Therefore, the flow rate of the water is approximately 0.117 m^3/s.
Now, let's move on to calculating the pressure in the water after it goes up a 5.2 m-high hill and flows in a 5.0 × 10^(-2)-m radius pipe.
To determine the pressure, we will use the equation:
P = P₀ + ρgh
Where:
P is the pressure in the water after it goes up the hill,
P₀ is the initial pressure of the water,
ρ is the density of water,
g is the acceleration due to gravity,
and h is the height of the hill.
Given that the initial pressure of the water is 2.2 × 10^5 N/m², the density of water is approximately 1000 kg/m³, the acceleration due to gravity is 9.8 m/s², and the height of the hill is 5.2 m, we can calculate the pressure after the hill:
Step 1: Calculate the pressure due to the height of the hill
P_hill = ρgh
P_hill = 1000 * 9.8 * 5.2
Step 2: Calculate the pressure after the hill
P = P₀ + P_hill
P = 2.2 × 10^5 + (1000 * 9.8 * 5.2)
Calculating the expression:
P ≈ 273450 N/m²
Therefore, the pressure in the water after it goes up the hill and flows in a 5.0 × 10^(-2)-m radius pipe is approximately 273450 N/m².
To find the flow rate of water, we can use the formula:
Flow Rate = Area × Velocity
where Area is the cross-sectional area of the pipe and Velocity is the speed of water.
1. Flow rate of the water:
Given:
Radius (r) = 6.5 × 10^(-2) m
Velocity (v) = 1.8 m/s
To find the area, we can use the formula:
Area = π × r^2
Substituting the given values:
Area = π × (6.5 × 10^(-2))^2
Calculate the area and substitute it into the formula for flow rate to find the answer.
2. Pressure in the water after it goes up the hill and flows in a different pipe:
Given:
Height (h) = 5.2 m
Radius (r) = 5.0 × 10^(-2) m
The pressure in the water can be found using the formula:
Pressure = Pressure_0 + ρgh
where Pressure_0 is the initial pressure, ρ is the density of water, g is the gravitational acceleration, and h is the height difference.
To find the final pressure, substitute the given values into the formula to get the answer.