Answer:
1.58 MPa
163 m
Explanation:
Given:
- Diameter @ inlet of nozzle D_i = 0.09 m
- Diameter @ exit of nozzle D_f = 0.03 m
- Flow rate of water through nozzle Q = 40 L /s
- Density of water p = 997 kg/m^3
Find:
a) Pressure drop in the nozzle (P_i - P_f)
- Compute Velocities at the two points V_i and V_f:
Q = A*V
40 / 1000 = pi*D_i^2 / 4 * V_i
V_i = (4*40) / (1000*pi*(0.09)^2)
V_i = 6.2876 m /s
V_f = (4*40) / (1000*pi*(0.03)^2)
V_i = 56.588 m /s
- Apply the Bernoulli's Equation:
(P_i - P_f) = 0.5*p* (V_f^2 - V_i^2)
dP = 0.5*997*(56.588^2 - 6.2876^2)
dP = 1.58 MPa
b) The maximum height the water can rise:
Assuming the water exits the nozzle as a free stream dP = 0
- Apply the Bernoulli's Equation:
p*g*h = 0.5*p* (V_f^2)
h = V^2_f / 2*g
h = (56.588)^2 / 2*9.81
h = 163 m
Answer:
The constant value is
The net displacement is
Explanation:
If the acceleration as a function of time is given then, first of all, knowing that the units of acceleration should be we should have where stands for The dimension of k (these are just the units of k in a less formal way of saying it.
On the other hand we have only information about the velocity, but we only have the acceleration function, it turns out we can integrate the expression of acceleration in order to obtain the velocity as a function of time:
where as a constant of integration which should have units of in order to be consistent with the fact that it is a velocity function, it is therefore natural to think of as the initial velocity of the the particle.
Let's now get our hands dirty by integrating
.
By having the velocity as a function of time we can now use the conditions given at t=0 and t=6.
At t=0 we have:
At t=6 the particle start reversing direction, that means at that very instant it velocity should be zero in order to start traveling the other way. This can only mean the following
.
We have a full description now of the acceleration and the velocity function. In order to get the net displacement we need to integrate the velocity function
Where is the initial displacement. If we subtract on both sides we get the net displacement or distance traveled
Plugging the value of 6 above gives us the net displacement
.
<h3>The correct Net force should be 2N becaues since the two forces 8N and 6N are going in different directions it would be subtraction so 8N-6N=2N . So the correct Net force is and should be 2N.</h3>
<em>I hope this helps :)!.</em>
Answer:
Explanation:
In projectile motion , formula for range is as follows
R = u² sin 2 α / g , where u is initial velocity of throw , α is angle of throw
Given R , range = 30 yards , α = 10°
30 = u² sin 20 / 9.8
u² x .342 = 294
u² = 859.65
u = 29.32 m / s