Fluid Mechanics Homework 4
NOTE: Use the given units in the problem for the whole problem. Do not convert units to a
different system. In the governing equation box, put the equations used in the problem. All
values should come from the book. Box your final answer. Show your work.
Problem 1
A two-dimensional velocity field is given by u = 1 + y and v = 1. Determine the equation of the streamline
that passes through the origin. On a graph, plot this streamline.
Governing Equation(s)
Problem 2
A certain flow field has the velocity vector as shown below. Find the x component of the acceleration
vector for this flow.
Governing Equation(s)
Problem 3
A fluid flows past a sphere with an upstream velocity of V0 = 40 m/s
as shown in Fig. P4.46. From a more advanced theory it is found
that the speed of the fluid along the front part of the sphere is
V = 3/2 V0 sin θ. Determine the streamwise(streamline) and normal
components of acceleration at point A if the radius of the sphere is
a = 0.20 m. Hint: ∂V/∂s = (∂V/∂Θ)( ∂Θ/ ∂s)
Governing Equation(s)
Problem 4
A gas flows along the x axis with a speed of V = 5x m/s and a pressure of p = 10x2 N/m2 , where x is in
meters. (a) Determine the time rate of change of pressure at the fixed location x = 1. (b) Determine the
time rate of change of pressure for a fluid particle flowing past x = 1. (You are foxed at x=1)
Governing Equation(s)
Problem 5
Air flows in a 15-cm-diameter horizontal pipe.
Determine (a) Determine the pressure at section 2
(Consider continuity and ideal gas law)
Start with Equation 5.22
Governing Equation(s)
( b) Determine the total friction force on the pipe wall (Consider the linear momentum equation)
Problem 6
Water flows as two free jets from the tee
attached to the pipe shown in the figure. The
exit speed is 15 m/s. If viscous effects and
gravity are negligible: Start with Equation
5.22
a) determine the inlet velocity in the pipe at
1?Governing Equation(s)
b) determine the pressure at 1 ?
Governing Equation(s)
c) determine the x and y components of the force that the pipe exerts on the tee?
Governing Equation(s)
Problem 7
(See The Wide World of Fluids article titled “Bow
Thrusters,” Section 5.2.2.) The bow thruster on the
boat shown in the figure is used to turn the boat. The
thruster produces a 1-m-diameter jet of water with a
velocity of 10 m/s. Determine the force produced by
the thruster. Assume that the inlet and outlet
pressures are zero and that the momentum of the water entering the thruster is negligible
Governing Equation(s)